Portfolio_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Portfolio Management"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I. Code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pandas version 0.25.1\n"
     ]
    }
   ],
   "source": [
    "import pandas_datareader.data as web\n",
    "from datetime import datetime, timedelta\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import datetime\n",
    "import scipy \n",
    "from scipy.stats import norm\n",
    "print(\"pandas version %s\" % pd.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_1 = pd.read_excel(\"Portfolio.xlsx\",sheet_name=\"Portfolio\")\n",
    "data_2 = pd.read_excel(\"Portfolio.xlsx\",sheet_name=\"Param\")\n",
    "data_3 = pd.read_excel(\"Portfolio.xlsx\",sheet_name=\"Sector\")\n",
    "data_4 = pd.read_excel(\"Portfolio.xlsx\",sheet_name=\"Rating\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>Exposure</th>\n",
       "      <th>Rating</th>\n",
       "      <th>LGD</th>\n",
       "      <th>Sector</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1894</td>\n",
       "      <td>1</td>\n",
       "      <td>0.59</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1095</td>\n",
       "      <td>4</td>\n",
       "      <td>0.44</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1627</td>\n",
       "      <td>6</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1914</td>\n",
       "      <td>10</td>\n",
       "      <td>0.57</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>1662</td>\n",
       "      <td>8</td>\n",
       "      <td>0.46</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id  Exposure  Rating   LGD  Sector\n",
       "0   1      1894       1  0.59       2\n",
       "1   2      1095       4  0.44       1\n",
       "2   3      1627       6  0.69       1\n",
       "3   4      1914      10  0.57       3\n",
       "4   5      1662       8  0.46       4"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Merge data in order to have maturity and correlation in the our portfolio dataframe "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "merged_portfolio = data_1.merge(data_4, how='left', on= 'Rating', sort=False).merge(data_3, how='left', on='Sector', sort=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>Exposure</th>\n",
       "      <th>Rating</th>\n",
       "      <th>LGD</th>\n",
       "      <th>Sector</th>\n",
       "      <th>1Y</th>\n",
       "      <th>3Y</th>\n",
       "      <th>5Y</th>\n",
       "      <th>Correlation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1894</td>\n",
       "      <td>1</td>\n",
       "      <td>0.59</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0015</td>\n",
       "      <td>0.00225</td>\n",
       "      <td>0.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1095</td>\n",
       "      <td>4</td>\n",
       "      <td>0.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.0240</td>\n",
       "      <td>0.03600</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1627</td>\n",
       "      <td>6</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.0540</td>\n",
       "      <td>0.08100</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1914</td>\n",
       "      <td>10</td>\n",
       "      <td>0.57</td>\n",
       "      <td>3</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>1662</td>\n",
       "      <td>8</td>\n",
       "      <td>0.46</td>\n",
       "      <td>4</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.0960</td>\n",
       "      <td>0.14400</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>95</td>\n",
       "      <td>96</td>\n",
       "      <td>1841</td>\n",
       "      <td>3</td>\n",
       "      <td>0.52</td>\n",
       "      <td>2</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.0135</td>\n",
       "      <td>0.02025</td>\n",
       "      <td>0.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>97</td>\n",
       "      <td>1779</td>\n",
       "      <td>2</td>\n",
       "      <td>0.40</td>\n",
       "      <td>4</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.0060</td>\n",
       "      <td>0.00900</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>98</td>\n",
       "      <td>1809</td>\n",
       "      <td>10</td>\n",
       "      <td>0.61</td>\n",
       "      <td>1</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>99</td>\n",
       "      <td>1737</td>\n",
       "      <td>7</td>\n",
       "      <td>0.46</td>\n",
       "      <td>3</td>\n",
       "      <td>0.049</td>\n",
       "      <td>0.0735</td>\n",
       "      <td>0.11025</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>100</td>\n",
       "      <td>1776</td>\n",
       "      <td>10</td>\n",
       "      <td>0.47</td>\n",
       "      <td>2</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.32</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Id  Exposure  Rating   LGD  Sector     1Y      3Y       5Y  Correlation\n",
       "0     1      1894       1  0.59       2  0.001  0.0015  0.00225         0.32\n",
       "1     2      1095       4  0.44       1  0.016  0.0240  0.03600         0.23\n",
       "2     3      1627       6  0.69       1  0.036  0.0540  0.08100         0.23\n",
       "3     4      1914      10  0.57       3  0.100  0.1500  0.22500         0.15\n",
       "4     5      1662       8  0.46       4  0.064  0.0960  0.14400         0.18\n",
       "..  ...       ...     ...   ...     ...    ...     ...      ...          ...\n",
       "95   96      1841       3  0.52       2  0.009  0.0135  0.02025         0.32\n",
       "96   97      1779       2  0.40       4  0.004  0.0060  0.00900         0.18\n",
       "97   98      1809      10  0.61       1  0.100  0.1500  0.22500         0.23\n",
       "98   99      1737       7  0.46       3  0.049  0.0735  0.11025         0.15\n",
       "99  100      1776      10  0.47       2  0.100  0.1500  0.22500         0.32\n",
       "\n",
       "[100 rows x 9 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged_portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set Id  as Index. Ids correspond to the 100 entities of our entire portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "merged_portfolio = merged_portfolio.set_index(merged_portfolio['Id'])\n",
    "merged_portfolio.sort_index(inplace=True)\n",
    "del merged_portfolio[\"Id\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exposure</th>\n",
       "      <th>Rating</th>\n",
       "      <th>LGD</th>\n",
       "      <th>Sector</th>\n",
       "      <th>1Y</th>\n",
       "      <th>3Y</th>\n",
       "      <th>5Y</th>\n",
       "      <th>Correlation</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1894</td>\n",
       "      <td>1</td>\n",
       "      <td>0.59</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0015</td>\n",
       "      <td>0.00225</td>\n",
       "      <td>0.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1095</td>\n",
       "      <td>4</td>\n",
       "      <td>0.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.0240</td>\n",
       "      <td>0.03600</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1627</td>\n",
       "      <td>6</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.0540</td>\n",
       "      <td>0.08100</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "</div>"
      ],
      "text/plain": [
       "    Exposure  Rating   LGD  Sector     1Y      3Y       5Y  Correlation\n",
       "Id                                                                     \n",
       "1       1894       1  0.59       2  0.001  0.0015  0.00225         0.32\n",
       "2       1095       4  0.44       1  0.016  0.0240  0.03600         0.23\n",
       "3       1627       6  0.69       1  0.036  0.0540  0.08100         0.23"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged_portfolio.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Monte Carlo simulation is a computational method that can be used for Portfolio Credit Risks. The approach is an example of using Simulation Models for the purpose of establishing a Risk Distribution. Once the distribution is obtained it is possible to estimate various risk measures for the credit portfolio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate(N_simu, N_entities, N_sectors):\n",
    "    #generate monte carlo simulation for X, the 100 entites and the 5 sectors\n",
    "    simulations = np.random.randn(N_simu, N_entities + N_sectors + 1)\n",
    "    #Convert to DataFrime\n",
    "    mydata = pd.DataFrame(simulations, index = [i for i in range(1,N_simu + 1)])\n",
    "    mydata.columns = ['X'] + ['X' +str(i) for i in range(1,N_sectors + 1)] + ['E' +str(i) for i in range(1, N_entities + 1)]\n",
    "    return mydata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DEFINE PARAMATERS\n",
    "N_simu = 10000\n",
    "N_entities = 100\n",
    "N_sectors = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>E1</th>\n",
       "      <th>E2</th>\n",
       "      <th>E3</th>\n",
       "      <th>E4</th>\n",
       "      <th>...</th>\n",
       "      <th>E91</th>\n",
       "      <th>E92</th>\n",
       "      <th>E93</th>\n",
       "      <th>E94</th>\n",
       "      <th>E95</th>\n",
       "      <th>E96</th>\n",
       "      <th>E97</th>\n",
       "      <th>E98</th>\n",
       "      <th>E99</th>\n",
       "      <th>E100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-0.516704</td>\n",
       "      <td>-0.293289</td>\n",
       "      <td>-1.646402</td>\n",
       "      <td>1.255794</td>\n",
       "      <td>0.361760</td>\n",
       "      <td>-2.116018</td>\n",
       "      <td>-1.265212</td>\n",
       "      <td>0.181041</td>\n",
       "      <td>-1.824586</td>\n",
       "      <td>0.175315</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.405518</td>\n",
       "      <td>0.023804</td>\n",
       "      <td>-0.239419</td>\n",
       "      <td>-1.896401</td>\n",
       "      <td>1.729116</td>\n",
       "      <td>1.584820</td>\n",
       "      <td>0.468026</td>\n",
       "      <td>0.403449</td>\n",
       "      <td>-0.057582</td>\n",
       "      <td>-0.698428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.731058</td>\n",
       "      <td>0.423532</td>\n",
       "      <td>0.249176</td>\n",
       "      <td>-0.907172</td>\n",
       "      <td>0.162770</td>\n",
       "      <td>1.578105</td>\n",
       "      <td>-1.835801</td>\n",
       "      <td>1.941728</td>\n",
       "      <td>0.680743</td>\n",
       "      <td>-0.899717</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.368619</td>\n",
       "      <td>0.853160</td>\n",
       "      <td>1.857797</td>\n",
       "      <td>-1.766308</td>\n",
       "      <td>-2.006284</td>\n",
       "      <td>0.598025</td>\n",
       "      <td>0.235974</td>\n",
       "      <td>0.191083</td>\n",
       "      <td>0.681968</td>\n",
       "      <td>1.073816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.295884</td>\n",
       "      <td>0.245099</td>\n",
       "      <td>-1.492979</td>\n",
       "      <td>-0.671457</td>\n",
       "      <td>-0.693417</td>\n",
       "      <td>0.005716</td>\n",
       "      <td>-0.012535</td>\n",
       "      <td>-0.280736</td>\n",
       "      <td>-0.813791</td>\n",
       "      <td>0.331873</td>\n",
       "      <td>...</td>\n",
       "      <td>2.444371</td>\n",
       "      <td>-0.830249</td>\n",
       "      <td>-0.101938</td>\n",
       "      <td>0.872858</td>\n",
       "      <td>0.943601</td>\n",
       "      <td>-0.797999</td>\n",
       "      <td>-1.628401</td>\n",
       "      <td>2.209689</td>\n",
       "      <td>-1.461621</td>\n",
       "      <td>0.893618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.450847</td>\n",
       "      <td>0.458072</td>\n",
       "      <td>-0.854475</td>\n",
       "      <td>-0.373334</td>\n",
       "      <td>1.300262</td>\n",
       "      <td>0.561679</td>\n",
       "      <td>0.147880</td>\n",
       "      <td>-0.789777</td>\n",
       "      <td>1.339788</td>\n",
       "      <td>0.776144</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.103121</td>\n",
       "      <td>0.337160</td>\n",
       "      <td>0.491314</td>\n",
       "      <td>1.550320</td>\n",
       "      <td>0.019692</td>\n",
       "      <td>-0.027581</td>\n",
       "      <td>1.905389</td>\n",
       "      <td>0.422113</td>\n",
       "      <td>0.417578</td>\n",
       "      <td>0.485641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>1.689560</td>\n",
       "      <td>-2.379968</td>\n",
       "      <td>-0.249060</td>\n",
       "      <td>0.816759</td>\n",
       "      <td>-0.660847</td>\n",
       "      <td>0.209427</td>\n",
       "      <td>-0.131171</td>\n",
       "      <td>-1.270558</td>\n",
       "      <td>0.979460</td>\n",
       "      <td>0.461240</td>\n",
       "      <td>...</td>\n",
       "      <td>0.561591</td>\n",
       "      <td>-1.348042</td>\n",
       "      <td>0.118746</td>\n",
       "      <td>1.418235</td>\n",
       "      <td>0.066224</td>\n",
       "      <td>0.264656</td>\n",
       "      <td>-0.573707</td>\n",
       "      <td>1.790835</td>\n",
       "      <td>1.754036</td>\n",
       "      <td>-0.012681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9996</td>\n",
       "      <td>-0.789543</td>\n",
       "      <td>0.800685</td>\n",
       "      <td>0.172017</td>\n",
       "      <td>-0.319245</td>\n",
       "      <td>-1.572092</td>\n",
       "      <td>0.091481</td>\n",
       "      <td>1.018860</td>\n",
       "      <td>1.309642</td>\n",
       "      <td>-0.610049</td>\n",
       "      <td>-0.761609</td>\n",
       "      <td>...</td>\n",
       "      <td>0.475843</td>\n",
       "      <td>0.045663</td>\n",
       "      <td>1.337451</td>\n",
       "      <td>-0.177070</td>\n",
       "      <td>-1.981225</td>\n",
       "      <td>-0.400378</td>\n",
       "      <td>-1.506539</td>\n",
       "      <td>0.424562</td>\n",
       "      <td>-0.433619</td>\n",
       "      <td>0.596619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9997</td>\n",
       "      <td>3.011834</td>\n",
       "      <td>-0.178033</td>\n",
       "      <td>-0.573538</td>\n",
       "      <td>1.421832</td>\n",
       "      <td>-0.194184</td>\n",
       "      <td>0.276499</td>\n",
       "      <td>-0.215347</td>\n",
       "      <td>-1.877191</td>\n",
       "      <td>-0.536837</td>\n",
       "      <td>-0.119310</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.572471</td>\n",
       "      <td>2.691436</td>\n",
       "      <td>1.739815</td>\n",
       "      <td>-0.826724</td>\n",
       "      <td>-0.770848</td>\n",
       "      <td>-0.752051</td>\n",
       "      <td>-0.250116</td>\n",
       "      <td>-0.033576</td>\n",
       "      <td>-0.049103</td>\n",
       "      <td>-0.045725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9998</td>\n",
       "      <td>1.134716</td>\n",
       "      <td>-0.526870</td>\n",
       "      <td>-1.868709</td>\n",
       "      <td>-0.600443</td>\n",
       "      <td>-0.196369</td>\n",
       "      <td>-0.755913</td>\n",
       "      <td>-0.280666</td>\n",
       "      <td>-0.096069</td>\n",
       "      <td>1.529460</td>\n",
       "      <td>1.059577</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.425378</td>\n",
       "      <td>-1.488585</td>\n",
       "      <td>-0.464290</td>\n",
       "      <td>0.485424</td>\n",
       "      <td>0.035516</td>\n",
       "      <td>1.669973</td>\n",
       "      <td>0.512996</td>\n",
       "      <td>-0.483964</td>\n",
       "      <td>0.750446</td>\n",
       "      <td>0.898754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9999</td>\n",
       "      <td>-3.069992</td>\n",
       "      <td>-0.743038</td>\n",
       "      <td>0.593919</td>\n",
       "      <td>0.657350</td>\n",
       "      <td>1.518217</td>\n",
       "      <td>-1.664055</td>\n",
       "      <td>-0.642910</td>\n",
       "      <td>0.153804</td>\n",
       "      <td>1.080328</td>\n",
       "      <td>-2.887922</td>\n",
       "      <td>...</td>\n",
       "      <td>2.047001</td>\n",
       "      <td>2.733990</td>\n",
       "      <td>-0.261326</td>\n",
       "      <td>0.061669</td>\n",
       "      <td>0.862954</td>\n",
       "      <td>0.023807</td>\n",
       "      <td>-2.069560</td>\n",
       "      <td>-1.947648</td>\n",
       "      <td>-0.460115</td>\n",
       "      <td>-1.362045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10000</td>\n",
       "      <td>0.422350</td>\n",
       "      <td>-0.851523</td>\n",
       "      <td>-0.190000</td>\n",
       "      <td>-0.405188</td>\n",
       "      <td>1.164940</td>\n",
       "      <td>0.633299</td>\n",
       "      <td>2.057476</td>\n",
       "      <td>-0.293932</td>\n",
       "      <td>-1.794188</td>\n",
       "      <td>0.067225</td>\n",
       "      <td>...</td>\n",
       "      <td>0.882237</td>\n",
       "      <td>-0.290098</td>\n",
       "      <td>1.530475</td>\n",
       "      <td>1.292462</td>\n",
       "      <td>-1.548156</td>\n",
       "      <td>-0.836005</td>\n",
       "      <td>-1.630746</td>\n",
       "      <td>0.710010</td>\n",
       "      <td>0.694111</td>\n",
       "      <td>-0.495900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 106 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              X        X1        X2        X3        X4        X5        E1  \\\n",
       "1     -0.516704 -0.293289 -1.646402  1.255794  0.361760 -2.116018 -1.265212   \n",
       "2      0.731058  0.423532  0.249176 -0.907172  0.162770  1.578105 -1.835801   \n",
       "3      0.295884  0.245099 -1.492979 -0.671457 -0.693417  0.005716 -0.012535   \n",
       "4      1.450847  0.458072 -0.854475 -0.373334  1.300262  0.561679  0.147880   \n",
       "5      1.689560 -2.379968 -0.249060  0.816759 -0.660847  0.209427 -0.131171   \n",
       "...         ...       ...       ...       ...       ...       ...       ...   \n",
       "9996  -0.789543  0.800685  0.172017 -0.319245 -1.572092  0.091481  1.018860   \n",
       "9997   3.011834 -0.178033 -0.573538  1.421832 -0.194184  0.276499 -0.215347   \n",
       "9998   1.134716 -0.526870 -1.868709 -0.600443 -0.196369 -0.755913 -0.280666   \n",
       "9999  -3.069992 -0.743038  0.593919  0.657350  1.518217 -1.664055 -0.642910   \n",
       "10000  0.422350 -0.851523 -0.190000 -0.405188  1.164940  0.633299  2.057476   \n",
       "\n",
       "             E2        E3        E4  ...       E91       E92       E93  \\\n",
       "1      0.181041 -1.824586  0.175315  ... -0.405518  0.023804 -0.239419   \n",
       "2      1.941728  0.680743 -0.899717  ... -0.368619  0.853160  1.857797   \n",
       "3     -0.280736 -0.813791  0.331873  ...  2.444371 -0.830249 -0.101938   \n",
       "4     -0.789777  1.339788  0.776144  ... -1.103121  0.337160  0.491314   \n",
       "5     -1.270558  0.979460  0.461240  ...  0.561591 -1.348042  0.118746   \n",
       "...         ...       ...       ...  ...       ...       ...       ...   \n",
       "9996   1.309642 -0.610049 -0.761609  ...  0.475843  0.045663  1.337451   \n",
       "9997  -1.877191 -0.536837 -0.119310  ... -0.572471  2.691436  1.739815   \n",
       "9998  -0.096069  1.529460  1.059577  ... -1.425378 -1.488585 -0.464290   \n",
       "9999   0.153804  1.080328 -2.887922  ...  2.047001  2.733990 -0.261326   \n",
       "10000 -0.293932 -1.794188  0.067225  ...  0.882237 -0.290098  1.530475   \n",
       "\n",
       "            E94       E95       E96       E97       E98       E99      E100  \n",
       "1     -1.896401  1.729116  1.584820  0.468026  0.403449 -0.057582 -0.698428  \n",
       "2     -1.766308 -2.006284  0.598025  0.235974  0.191083  0.681968  1.073816  \n",
       "3      0.872858  0.943601 -0.797999 -1.628401  2.209689 -1.461621  0.893618  \n",
       "4      1.550320  0.019692 -0.027581  1.905389  0.422113  0.417578  0.485641  \n",
       "5      1.418235  0.066224  0.264656 -0.573707  1.790835  1.754036 -0.012681  \n",
       "...         ...       ...       ...       ...       ...       ...       ...  \n",
       "9996  -0.177070 -1.981225 -0.400378 -1.506539  0.424562 -0.433619  0.596619  \n",
       "9997  -0.826724 -0.770848 -0.752051 -0.250116 -0.033576 -0.049103 -0.045725  \n",
       "9998   0.485424  0.035516  1.669973  0.512996 -0.483964  0.750446  0.898754  \n",
       "9999   0.061669  0.862954  0.023807 -2.069560 -1.947648 -0.460115 -1.362045  \n",
       "10000  1.292462 -1.548156 -0.836005 -1.630746  0.710010  0.694111 -0.495900  \n",
       "\n",
       "[10000 rows x 106 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Generate Simulations \n",
    "mydata = generate(N_simu, N_entities, N_sectors)\n",
    "mydata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>E1</th>\n",
       "      <th>E2</th>\n",
       "      <th>E3</th>\n",
       "      <th>E4</th>\n",
       "      <th>...</th>\n",
       "      <th>E91</th>\n",
       "      <th>E92</th>\n",
       "      <th>E93</th>\n",
       "      <th>E94</th>\n",
       "      <th>E95</th>\n",
       "      <th>E96</th>\n",
       "      <th>E97</th>\n",
       "      <th>E98</th>\n",
       "      <th>E99</th>\n",
       "      <th>E100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>-0.001009</td>\n",
       "      <td>-0.010051</td>\n",
       "      <td>0.006356</td>\n",
       "      <td>-0.005010</td>\n",
       "      <td>-0.000923</td>\n",
       "      <td>0.000411</td>\n",
       "      <td>0.003865</td>\n",
       "      <td>-0.004089</td>\n",
       "      <td>-0.004833</td>\n",
       "      <td>-0.002203</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.006506</td>\n",
       "      <td>-0.009435</td>\n",
       "      <td>-0.001981</td>\n",
       "      <td>0.009310</td>\n",
       "      <td>0.012946</td>\n",
       "      <td>0.005973</td>\n",
       "      <td>0.006372</td>\n",
       "      <td>0.010955</td>\n",
       "      <td>-0.020193</td>\n",
       "      <td>0.000973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>1.014165</td>\n",
       "      <td>1.001077</td>\n",
       "      <td>1.007655</td>\n",
       "      <td>0.995248</td>\n",
       "      <td>0.996059</td>\n",
       "      <td>1.000377</td>\n",
       "      <td>0.991766</td>\n",
       "      <td>0.995806</td>\n",
       "      <td>1.006337</td>\n",
       "      <td>1.001888</td>\n",
       "      <td>...</td>\n",
       "      <td>1.005694</td>\n",
       "      <td>0.994139</td>\n",
       "      <td>1.002500</td>\n",
       "      <td>1.004282</td>\n",
       "      <td>1.011108</td>\n",
       "      <td>0.999557</td>\n",
       "      <td>0.999449</td>\n",
       "      <td>0.996899</td>\n",
       "      <td>1.003898</td>\n",
       "      <td>0.997574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>-4.460845</td>\n",
       "      <td>-3.548837</td>\n",
       "      <td>-3.734617</td>\n",
       "      <td>-3.688907</td>\n",
       "      <td>-4.009585</td>\n",
       "      <td>-4.211877</td>\n",
       "      <td>-3.828562</td>\n",
       "      <td>-3.756666</td>\n",
       "      <td>-4.622964</td>\n",
       "      <td>-3.688267</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.893913</td>\n",
       "      <td>-3.609809</td>\n",
       "      <td>-3.572000</td>\n",
       "      <td>-3.545014</td>\n",
       "      <td>-3.793536</td>\n",
       "      <td>-3.983030</td>\n",
       "      <td>-4.197417</td>\n",
       "      <td>-3.863337</td>\n",
       "      <td>-3.336404</td>\n",
       "      <td>-3.419254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>-0.687164</td>\n",
       "      <td>-0.698190</td>\n",
       "      <td>-0.670636</td>\n",
       "      <td>-0.677875</td>\n",
       "      <td>-0.671628</td>\n",
       "      <td>-0.666653</td>\n",
       "      <td>-0.665110</td>\n",
       "      <td>-0.677345</td>\n",
       "      <td>-0.695432</td>\n",
       "      <td>-0.664614</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.681540</td>\n",
       "      <td>-0.687571</td>\n",
       "      <td>-0.673218</td>\n",
       "      <td>-0.683812</td>\n",
       "      <td>-0.679538</td>\n",
       "      <td>-0.667866</td>\n",
       "      <td>-0.668525</td>\n",
       "      <td>-0.658038</td>\n",
       "      <td>-0.697184</td>\n",
       "      <td>-0.674091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>0.002456</td>\n",
       "      <td>-0.029893</td>\n",
       "      <td>0.019203</td>\n",
       "      <td>-0.017440</td>\n",
       "      <td>-0.005322</td>\n",
       "      <td>0.002028</td>\n",
       "      <td>-0.004770</td>\n",
       "      <td>0.001268</td>\n",
       "      <td>0.002888</td>\n",
       "      <td>-0.006373</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.005722</td>\n",
       "      <td>-0.011217</td>\n",
       "      <td>0.000630</td>\n",
       "      <td>0.005659</td>\n",
       "      <td>0.011571</td>\n",
       "      <td>0.015570</td>\n",
       "      <td>0.006614</td>\n",
       "      <td>0.005523</td>\n",
       "      <td>-0.018451</td>\n",
       "      <td>0.001537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>0.682574</td>\n",
       "      <td>0.666347</td>\n",
       "      <td>0.686332</td>\n",
       "      <td>0.672838</td>\n",
       "      <td>0.682662</td>\n",
       "      <td>0.680912</td>\n",
       "      <td>0.666893</td>\n",
       "      <td>0.664092</td>\n",
       "      <td>0.674347</td>\n",
       "      <td>0.672283</td>\n",
       "      <td>...</td>\n",
       "      <td>0.680090</td>\n",
       "      <td>0.663607</td>\n",
       "      <td>0.684188</td>\n",
       "      <td>0.683132</td>\n",
       "      <td>0.709661</td>\n",
       "      <td>0.681918</td>\n",
       "      <td>0.675312</td>\n",
       "      <td>0.693518</td>\n",
       "      <td>0.658700</td>\n",
       "      <td>0.655739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>4.131283</td>\n",
       "      <td>3.865593</td>\n",
       "      <td>3.978795</td>\n",
       "      <td>3.880629</td>\n",
       "      <td>3.790968</td>\n",
       "      <td>3.712794</td>\n",
       "      <td>4.465736</td>\n",
       "      <td>3.524877</td>\n",
       "      <td>4.102192</td>\n",
       "      <td>3.888847</td>\n",
       "      <td>...</td>\n",
       "      <td>3.797745</td>\n",
       "      <td>3.232363</td>\n",
       "      <td>4.054817</td>\n",
       "      <td>3.629523</td>\n",
       "      <td>3.725042</td>\n",
       "      <td>4.138324</td>\n",
       "      <td>3.520184</td>\n",
       "      <td>3.854354</td>\n",
       "      <td>3.614944</td>\n",
       "      <td>3.803561</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 106 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  X            X1            X2            X3            X4  \\\n",
       "count  10000.000000  10000.000000  10000.000000  10000.000000  10000.000000   \n",
       "mean      -0.001009     -0.010051      0.006356     -0.005010     -0.000923   \n",
       "std        1.014165      1.001077      1.007655      0.995248      0.996059   \n",
       "min       -4.460845     -3.548837     -3.734617     -3.688907     -4.009585   \n",
       "25%       -0.687164     -0.698190     -0.670636     -0.677875     -0.671628   \n",
       "50%        0.002456     -0.029893      0.019203     -0.017440     -0.005322   \n",
       "75%        0.682574      0.666347      0.686332      0.672838      0.682662   \n",
       "max        4.131283      3.865593      3.978795      3.880629      3.790968   \n",
       "\n",
       "                 X5            E1            E2            E3            E4  \\\n",
       "count  10000.000000  10000.000000  10000.000000  10000.000000  10000.000000   \n",
       "mean       0.000411      0.003865     -0.004089     -0.004833     -0.002203   \n",
       "std        1.000377      0.991766      0.995806      1.006337      1.001888   \n",
       "min       -4.211877     -3.828562     -3.756666     -4.622964     -3.688267   \n",
       "25%       -0.666653     -0.665110     -0.677345     -0.695432     -0.664614   \n",
       "50%        0.002028     -0.004770      0.001268      0.002888     -0.006373   \n",
       "75%        0.680912      0.666893      0.664092      0.674347      0.672283   \n",
       "max        3.712794      4.465736      3.524877      4.102192      3.888847   \n",
       "\n",
       "       ...           E91           E92           E93           E94  \\\n",
       "count  ...  10000.000000  10000.000000  10000.000000  10000.000000   \n",
       "mean   ...     -0.006506     -0.009435     -0.001981      0.009310   \n",
       "std    ...      1.005694      0.994139      1.002500      1.004282   \n",
       "min    ...     -3.893913     -3.609809     -3.572000     -3.545014   \n",
       "25%    ...     -0.681540     -0.687571     -0.673218     -0.683812   \n",
       "50%    ...     -0.005722     -0.011217      0.000630      0.005659   \n",
       "75%    ...      0.680090      0.663607      0.684188      0.683132   \n",
       "max    ...      3.797745      3.232363      4.054817      3.629523   \n",
       "\n",
       "                E95           E96           E97           E98           E99  \\\n",
       "count  10000.000000  10000.000000  10000.000000  10000.000000  10000.000000   \n",
       "mean       0.012946      0.005973      0.006372      0.010955     -0.020193   \n",
       "std        1.011108      0.999557      0.999449      0.996899      1.003898   \n",
       "min       -3.793536     -3.983030     -4.197417     -3.863337     -3.336404   \n",
       "25%       -0.679538     -0.667866     -0.668525     -0.658038     -0.697184   \n",
       "50%        0.011571      0.015570      0.006614      0.005523     -0.018451   \n",
       "75%        0.709661      0.681918      0.675312      0.693518      0.658700   \n",
       "max        3.725042      4.138324      3.520184      3.854354      3.614944   \n",
       "\n",
       "               E100  \n",
       "count  10000.000000  \n",
       "mean       0.000973  \n",
       "std        0.997574  \n",
       "min       -3.419254  \n",
       "25%       -0.674091  \n",
       "50%        0.001537  \n",
       "75%        0.655739  \n",
       "max        3.803561  \n",
       "\n",
       "[8 rows x 106 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mydata.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Default Model : MG2F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_Z(simu_df, N_entities, N_simu, rho):\n",
    "    #create the dataframe with nan values\n",
    "    default = pd.DataFrame(columns=['Z' +str(i) for i in range(1, N_entities + 1)], index = [i for i in range(1, N_simu + 1)])\n",
    "    #compute Z\n",
    "    for i in range(1,N_entities + 1):\n",
    "        default['Z' +str(i)] = np.sqrt(rho) * simu_df['X'] + np.sqrt(1 - merged_portfolio['Correlation'][i]) * simu_df['E' +str(i)] + np.sqrt(merged_portfolio['Correlation'][i]-rho)*simu_df['X' +str(merged_portfolio['Sector'][i])]\n",
    "    return default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z3</th>\n",
       "      <th>Z4</th>\n",
       "      <th>Z5</th>\n",
       "      <th>Z6</th>\n",
       "      <th>Z7</th>\n",
       "      <th>Z8</th>\n",
       "      <th>Z9</th>\n",
       "      <th>Z10</th>\n",
       "      <th>...</th>\n",
       "      <th>Z91</th>\n",
       "      <th>Z92</th>\n",
       "      <th>Z93</th>\n",
       "      <th>Z94</th>\n",
       "      <th>Z95</th>\n",
       "      <th>Z96</th>\n",
       "      <th>Z97</th>\n",
       "      <th>Z98</th>\n",
       "      <th>Z99</th>\n",
       "      <th>Z100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-1.969168</td>\n",
       "      <td>-0.114107</td>\n",
       "      <td>-1.874038</td>\n",
       "      <td>0.241420</td>\n",
       "      <td>-1.646855</td>\n",
       "      <td>-1.261163</td>\n",
       "      <td>-0.104154</td>\n",
       "      <td>-1.992881</td>\n",
       "      <td>-0.994517</td>\n",
       "      <td>-1.077367</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.168883</td>\n",
       "      <td>-0.054103</td>\n",
       "      <td>-1.020320</td>\n",
       "      <td>-2.502369</td>\n",
       "      <td>1.244323</td>\n",
       "      <td>0.381029</td>\n",
       "      <td>0.348157</td>\n",
       "      <td>0.081055</td>\n",
       "      <td>0.026699</td>\n",
       "      <td>-1.501786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-1.157189</td>\n",
       "      <td>2.093040</td>\n",
       "      <td>0.986529</td>\n",
       "      <td>-0.768468</td>\n",
       "      <td>1.527835</td>\n",
       "      <td>0.493578</td>\n",
       "      <td>0.483953</td>\n",
       "      <td>-0.725671</td>\n",
       "      <td>-1.330526</td>\n",
       "      <td>-0.243337</td>\n",
       "      <td>...</td>\n",
       "      <td>0.386193</td>\n",
       "      <td>1.058099</td>\n",
       "      <td>2.377560</td>\n",
       "      <td>-0.863938</td>\n",
       "      <td>-1.371327</td>\n",
       "      <td>0.849795</td>\n",
       "      <td>0.499212</td>\n",
       "      <td>0.556855</td>\n",
       "      <td>0.689773</td>\n",
       "      <td>1.242143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>-0.596372</td>\n",
       "      <td>-0.063306</td>\n",
       "      <td>-0.531061</td>\n",
       "      <td>0.269814</td>\n",
       "      <td>-0.359192</td>\n",
       "      <td>0.192915</td>\n",
       "      <td>-0.607894</td>\n",
       "      <td>-0.096600</td>\n",
       "      <td>0.972625</td>\n",
       "      <td>-0.426451</td>\n",
       "      <td>...</td>\n",
       "      <td>2.286161</td>\n",
       "      <td>-0.837150</td>\n",
       "      <td>0.008672</td>\n",
       "      <td>0.880557</td>\n",
       "      <td>1.011045</td>\n",
       "      <td>-1.244082</td>\n",
       "      <td>-1.559907</td>\n",
       "      <td>2.122033</td>\n",
       "      <td>-1.383706</td>\n",
       "      <td>0.150861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.211567</td>\n",
       "      <td>-0.053154</td>\n",
       "      <td>1.815532</td>\n",
       "      <td>1.122095</td>\n",
       "      <td>1.935959</td>\n",
       "      <td>-0.425040</td>\n",
       "      <td>0.294678</td>\n",
       "      <td>-0.442046</td>\n",
       "      <td>-0.744247</td>\n",
       "      <td>-0.488238</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.336966</td>\n",
       "      <td>1.130520</td>\n",
       "      <td>1.089140</td>\n",
       "      <td>2.036344</td>\n",
       "      <td>0.657152</td>\n",
       "      <td>0.066878</td>\n",
       "      <td>2.550612</td>\n",
       "      <td>1.010275</td>\n",
       "      <td>0.791513</td>\n",
       "      <td>0.490092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.338063</td>\n",
       "      <td>-1.378992</td>\n",
       "      <td>0.595391</td>\n",
       "      <td>1.148958</td>\n",
       "      <td>-0.447941</td>\n",
       "      <td>-1.403186</td>\n",
       "      <td>0.864782</td>\n",
       "      <td>0.873467</td>\n",
       "      <td>1.546911</td>\n",
       "      <td>0.545442</td>\n",
       "      <td>...</td>\n",
       "      <td>1.125494</td>\n",
       "      <td>-0.835184</td>\n",
       "      <td>0.729401</td>\n",
       "      <td>1.891699</td>\n",
       "      <td>-0.205970</td>\n",
       "      <td>0.664471</td>\n",
       "      <td>-0.133994</td>\n",
       "      <td>1.307370</td>\n",
       "      <td>2.340856</td>\n",
       "      <td>0.435773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9996</td>\n",
       "      <td>0.657140</td>\n",
       "      <td>1.164710</td>\n",
       "      <td>-0.519812</td>\n",
       "      <td>-1.027880</td>\n",
       "      <td>-0.925312</td>\n",
       "      <td>1.037947</td>\n",
       "      <td>0.805744</td>\n",
       "      <td>-0.430146</td>\n",
       "      <td>-1.399831</td>\n",
       "      <td>-0.836215</td>\n",
       "      <td>...</td>\n",
       "      <td>0.191190</td>\n",
       "      <td>-0.636449</td>\n",
       "      <td>0.961835</td>\n",
       "      <td>-0.392793</td>\n",
       "      <td>-1.723015</td>\n",
       "      <td>-0.513194</td>\n",
       "      <td>-2.042027</td>\n",
       "      <td>0.388055</td>\n",
       "      <td>-0.725488</td>\n",
       "      <td>0.308950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9997</td>\n",
       "      <td>0.558505</td>\n",
       "      <td>-0.709989</td>\n",
       "      <td>0.466168</td>\n",
       "      <td>1.173280</td>\n",
       "      <td>0.519448</td>\n",
       "      <td>1.558809</td>\n",
       "      <td>2.391168</td>\n",
       "      <td>1.820223</td>\n",
       "      <td>1.607621</td>\n",
       "      <td>1.795257</td>\n",
       "      <td>...</td>\n",
       "      <td>0.569828</td>\n",
       "      <td>3.384735</td>\n",
       "      <td>2.638000</td>\n",
       "      <td>0.342417</td>\n",
       "      <td>0.260824</td>\n",
       "      <td>0.115927</td>\n",
       "      <td>0.721046</td>\n",
       "      <td>0.907777</td>\n",
       "      <td>1.238008</td>\n",
       "      <td>0.698378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9998</td>\n",
       "      <td>-0.711451</td>\n",
       "      <td>0.109529</td>\n",
       "      <td>1.535925</td>\n",
       "      <td>1.233136</td>\n",
       "      <td>1.693594</td>\n",
       "      <td>1.106576</td>\n",
       "      <td>-0.695231</td>\n",
       "      <td>-0.363921</td>\n",
       "      <td>-0.557251</td>\n",
       "      <td>-0.680188</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.125328</td>\n",
       "      <td>-1.023583</td>\n",
       "      <td>-0.265705</td>\n",
       "      <td>0.583745</td>\n",
       "      <td>0.224995</td>\n",
       "      <td>0.897088</td>\n",
       "      <td>0.788926</td>\n",
       "      <td>-0.230847</td>\n",
       "      <td>0.948132</td>\n",
       "      <td>0.261124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9999</td>\n",
       "      <td>-1.276191</td>\n",
       "      <td>-1.140634</td>\n",
       "      <td>-0.327613</td>\n",
       "      <td>-3.549264</td>\n",
       "      <td>-0.677553</td>\n",
       "      <td>-0.302779</td>\n",
       "      <td>-2.166445</td>\n",
       "      <td>-2.079094</td>\n",
       "      <td>-1.087462</td>\n",
       "      <td>-3.481880</td>\n",
       "      <td>...</td>\n",
       "      <td>0.313475</td>\n",
       "      <td>1.859215</td>\n",
       "      <td>-1.751155</td>\n",
       "      <td>-1.462259</td>\n",
       "      <td>-0.518358</td>\n",
       "      <td>-0.726402</td>\n",
       "      <td>-2.490585</td>\n",
       "      <td>-2.984652</td>\n",
       "      <td>-1.310936</td>\n",
       "      <td>-1.869205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10000</td>\n",
       "      <td>1.749647</td>\n",
       "      <td>-0.412823</td>\n",
       "      <td>-1.729292</td>\n",
       "      <td>0.121018</td>\n",
       "      <td>-0.308388</td>\n",
       "      <td>0.185305</td>\n",
       "      <td>-0.695008</td>\n",
       "      <td>1.281241</td>\n",
       "      <td>1.398783</td>\n",
       "      <td>0.347591</td>\n",
       "      <td>...</td>\n",
       "      <td>1.119164</td>\n",
       "      <td>0.185597</td>\n",
       "      <td>1.698966</td>\n",
       "      <td>1.486080</td>\n",
       "      <td>-1.513400</td>\n",
       "      <td>-0.636379</td>\n",
       "      <td>-1.028411</td>\n",
       "      <td>0.468132</td>\n",
       "      <td>0.698979</td>\n",
       "      <td>-0.355920</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 100 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Z1        Z2        Z3        Z4        Z5        Z6        Z7  \\\n",
       "1     -1.969168 -0.114107 -1.874038  0.241420 -1.646855 -1.261163 -0.104154   \n",
       "2     -1.157189  2.093040  0.986529 -0.768468  1.527835  0.493578  0.483953   \n",
       "3     -0.596372 -0.063306 -0.531061  0.269814 -0.359192  0.192915 -0.607894   \n",
       "4      0.211567 -0.053154  1.815532  1.122095  1.935959 -0.425040  0.294678   \n",
       "5      0.338063 -1.378992  0.595391  1.148958 -0.447941 -1.403186  0.864782   \n",
       "...         ...       ...       ...       ...       ...       ...       ...   \n",
       "9996   0.657140  1.164710 -0.519812 -1.027880 -0.925312  1.037947  0.805744   \n",
       "9997   0.558505 -0.709989  0.466168  1.173280  0.519448  1.558809  2.391168   \n",
       "9998  -0.711451  0.109529  1.535925  1.233136  1.693594  1.106576 -0.695231   \n",
       "9999  -1.276191 -1.140634 -0.327613 -3.549264 -0.677553 -0.302779 -2.166445   \n",
       "10000  1.749647 -0.412823 -1.729292  0.121018 -0.308388  0.185305 -0.695008   \n",
       "\n",
       "             Z8        Z9       Z10  ...       Z91       Z92       Z93  \\\n",
       "1     -1.992881 -0.994517 -1.077367  ... -1.168883 -0.054103 -1.020320   \n",
       "2     -0.725671 -1.330526 -0.243337  ...  0.386193  1.058099  2.377560   \n",
       "3     -0.096600  0.972625 -0.426451  ...  2.286161 -0.837150  0.008672   \n",
       "4     -0.442046 -0.744247 -0.488238  ... -0.336966  1.130520  1.089140   \n",
       "5      0.873467  1.546911  0.545442  ...  1.125494 -0.835184  0.729401   \n",
       "...         ...       ...       ...  ...       ...       ...       ...   \n",
       "9996  -0.430146 -1.399831 -0.836215  ...  0.191190 -0.636449  0.961835   \n",
       "9997   1.820223  1.607621  1.795257  ...  0.569828  3.384735  2.638000   \n",
       "9998  -0.363921 -0.557251 -0.680188  ... -1.125328 -1.023583 -0.265705   \n",
       "9999  -2.079094 -1.087462 -3.481880  ...  0.313475  1.859215 -1.751155   \n",
       "10000  1.281241  1.398783  0.347591  ...  1.119164  0.185597  1.698966   \n",
       "\n",
       "            Z94       Z95       Z96       Z97       Z98       Z99      Z100  \n",
       "1     -2.502369  1.244323  0.381029  0.348157  0.081055  0.026699 -1.501786  \n",
       "2     -0.863938 -1.371327  0.849795  0.499212  0.556855  0.689773  1.242143  \n",
       "3      0.880557  1.011045 -1.244082 -1.559907  2.122033 -1.383706  0.150861  \n",
       "4      2.036344  0.657152  0.066878  2.550612  1.010275  0.791513  0.490092  \n",
       "5      1.891699 -0.205970  0.664471 -0.133994  1.307370  2.340856  0.435773  \n",
       "...         ...       ...       ...       ...       ...       ...       ...  \n",
       "9996  -0.392793 -1.723015 -0.513194 -2.042027  0.388055 -0.725488  0.308950  \n",
       "9997   0.342417  0.260824  0.115927  0.721046  0.907777  1.238008  0.698378  \n",
       "9998   0.583745  0.224995  0.897088  0.788926 -0.230847  0.948132  0.261124  \n",
       "9999  -1.462259 -0.518358 -0.726402 -2.490585 -2.984652 -1.310936 -1.869205  \n",
       "10000  1.486080 -1.513400 -0.636379 -1.028411  0.468132  0.698979 -0.355920  \n",
       "\n",
       "[10000 rows x 100 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "default = compute_Z(mydata, 100, 10000, 0.11)\n",
    "default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Barrier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Compute barrier\n",
    "def compute_barrier(portfolio, maturity):\n",
    "    portfolio['Barrier' + maturity] = norm.ppf(portfolio[maturity])\n",
    "    return portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exposure</th>\n",
       "      <th>Rating</th>\n",
       "      <th>LGD</th>\n",
       "      <th>Sector</th>\n",
       "      <th>1Y</th>\n",
       "      <th>3Y</th>\n",
       "      <th>5Y</th>\n",
       "      <th>Correlation</th>\n",
       "      <th>Barrier1Y</th>\n",
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       "      <th></th>\n",
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       "      <td>0.23</td>\n",
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       "      <td>3</td>\n",
       "      <td>1627</td>\n",
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       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.0540</td>\n",
       "      <td>0.08100</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-1.799118</td>\n",
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       "      <td>4</td>\n",
       "      <td>1914</td>\n",
       "      <td>10</td>\n",
       "      <td>0.57</td>\n",
       "      <td>3</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.15</td>\n",
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       "      <td>96</td>\n",
       "      <td>1841</td>\n",
       "      <td>3</td>\n",
       "      <td>0.52</td>\n",
       "      <td>2</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.0135</td>\n",
       "      <td>0.02025</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-2.365618</td>\n",
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       "    <tr>\n",
       "      <td>97</td>\n",
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       "      <td>0.00900</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-2.652070</td>\n",
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       "      <td>98</td>\n",
       "      <td>1809</td>\n",
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       "</table>\n",
       "<p>100 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Exposure  Rating   LGD  Sector     1Y      3Y       5Y  Correlation  \\\n",
       "Id                                                                         \n",
       "1        1894       1  0.59       2  0.001  0.0015  0.00225         0.32   \n",
       "2        1095       4  0.44       1  0.016  0.0240  0.03600         0.23   \n",
       "3        1627       6  0.69       1  0.036  0.0540  0.08100         0.23   \n",
       "4        1914      10  0.57       3  0.100  0.1500  0.22500         0.15   \n",
       "5        1662       8  0.46       4  0.064  0.0960  0.14400         0.18   \n",
       "..        ...     ...   ...     ...    ...     ...      ...          ...   \n",
       "96       1841       3  0.52       2  0.009  0.0135  0.02025         0.32   \n",
       "97       1779       2  0.40       4  0.004  0.0060  0.00900         0.18   \n",
       "98       1809      10  0.61       1  0.100  0.1500  0.22500         0.23   \n",
       "99       1737       7  0.46       3  0.049  0.0735  0.11025         0.15   \n",
       "100      1776      10  0.47       2  0.100  0.1500  0.22500         0.32   \n",
       "\n",
       "     Barrier1Y  \n",
       "Id              \n",
       "1    -3.090232  \n",
       "2    -2.144411  \n",
       "3    -1.799118  \n",
       "4    -1.281552  \n",
       "5    -1.522036  \n",
       "..         ...  \n",
       "96   -2.365618  \n",
       "97   -2.652070  \n",
       "98   -1.281552  \n",
       "99   -1.654628  \n",
       "100  -1.281552  \n",
       "\n",
       "[100 rows x 9 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myportfolio = compute_barrier(merged_portfolio, '1Y')\n",
    "myportfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# When default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def whendefault(myportfolio,default, N_entities, N_simu, maturity):\n",
    "    df = pd.DataFrame(columns=['D' +str(i) for i in range(1, N_entities + 1)], index = [i for i in range(1, N_simu + 1)])\n",
    "    for i in range(1, N_entities + 1):\n",
    "        df['D' +str(i)] = default['Z' +str(i)].apply(lambda x: 1 if x <= myportfolio['Barrier' + maturity][i] else 0)\n",
    "    return df    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9997</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9998</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9999</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 100 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       D1  D2  D3  D4  D5  D6  D7  D8  D9  D10  ...  D91  D92  D93  D94  D95  \\\n",
       "1       0   0   1   0   1   0   0   0   0    0  ...    0    0    0    1    0   \n",
       "2       0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    0   \n",
       "3       0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    0   \n",
       "4       0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    0   \n",
       "5       0   0   0   0   0   1   0   0   0    0  ...    0    0    0    0    0   \n",
       "...    ..  ..  ..  ..  ..  ..  ..  ..  ..  ...  ...  ...  ...  ...  ...  ...   \n",
       "9996    0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    1   \n",
       "9997    0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    0   \n",
       "9998    0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    0   \n",
       "9999    0   0   0   1   0   0   1   0   0    1  ...    0    0    1    1    0   \n",
       "10000   0   0   0   0   0   0   0   0   0    0  ...    0    0    0    0    0   \n",
       "\n",
       "       D96  D97  D98  D99  D100  \n",
       "1        0    0    0    0     1  \n",
       "2        0    0    0    0     0  \n",
       "3        0    0    0    0     0  \n",
       "4        0    0    0    0     0  \n",
       "5        0    0    0    0     0  \n",
       "...    ...  ...  ...  ...   ...  \n",
       "9996     0    0    0    0     0  \n",
       "9997     0    0    0    0     0  \n",
       "9998     0    0    0    0     0  \n",
       "9999     0    0    1    0     1  \n",
       "10000    0    0    0    0     0  \n",
       "\n",
       "[10000 rows x 100 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "default_df = whendefault(myportfolio,default, N_entities, N_simu, '1Y')\n",
    "default_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute Losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#compute simualtion loss dataframe\n",
    "def compute_loss(myportfolio, default_df, N_entities):\n",
    "    loss_df = default_df.copy()\n",
    "    loss_df.columns = ['Loss' +str(i) for i in range(1, N_entities + 1)]\n",
    "    for i in range(1, N_entities + 1):\n",
    "        loss_df['Loss' +str(i)] = default_df['D' +str(i)].apply(lambda x: x * myportfolio['Exposure'][i] * myportfolio['LGD'][i])\n",
    "    return loss_df     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Loss1</th>\n",
       "      <th>Loss2</th>\n",
       "      <th>Loss3</th>\n",
       "      <th>Loss4</th>\n",
       "      <th>Loss5</th>\n",
       "      <th>Loss6</th>\n",
       "      <th>Loss7</th>\n",
       "      <th>Loss8</th>\n",
       "      <th>Loss9</th>\n",
       "      <th>Loss10</th>\n",
       "      <th>...</th>\n",
       "      <th>Loss91</th>\n",
       "      <th>Loss92</th>\n",
       "      <th>Loss93</th>\n",
       "      <th>Loss94</th>\n",
       "      <th>Loss95</th>\n",
       "      <th>Loss96</th>\n",
       "      <th>Loss97</th>\n",
       "      <th>Loss98</th>\n",
       "      <th>Loss99</th>\n",
       "      <th>Loss100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1122.63</td>\n",
       "      <td>0.00</td>\n",
       "      <td>764.52</td>\n",
       "      <td>0.00</td>\n",
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       "      <td>896.56</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>834.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
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       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>968.49</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <td>9996</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1359.36</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
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       "    <tr>\n",
       "      <td>9997</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9998</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9999</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1090.98</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>908.44</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1251.2</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>834.36</td>\n",
       "      <td>896.56</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1103.49</td>\n",
       "      <td>0.0</td>\n",
       "      <td>834.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 100 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Loss1  Loss2    Loss3    Loss4   Loss5   Loss6   Loss7  Loss8  Loss9  \\\n",
       "1        0.0    0.0  1122.63     0.00  764.52    0.00    0.00    0.0    0.0   \n",
       "2        0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "3        0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "4        0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "5        0.0    0.0     0.00     0.00    0.00  968.49    0.00    0.0    0.0   \n",
       "...      ...    ...      ...      ...     ...     ...     ...    ...    ...   \n",
       "9996     0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "9997     0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "9998     0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "9999     0.0    0.0     0.00  1090.98    0.00    0.00  908.44    0.0    0.0   \n",
       "10000    0.0    0.0     0.00     0.00    0.00    0.00    0.00    0.0    0.0   \n",
       "\n",
       "       Loss10  ...  Loss91  Loss92  Loss93  Loss94   Loss95  Loss96  Loss97  \\\n",
       "1         0.0  ...     0.0     0.0    0.00  896.56     0.00     0.0     0.0   \n",
       "2         0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "3         0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "4         0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "5         0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "...       ...  ...     ...     ...     ...     ...      ...     ...     ...   \n",
       "9996      0.0  ...     0.0     0.0    0.00    0.00  1359.36     0.0     0.0   \n",
       "9997      0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "9998      0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "9999   1251.2  ...     0.0     0.0  834.36  896.56     0.00     0.0     0.0   \n",
       "10000     0.0  ...     0.0     0.0    0.00    0.00     0.00     0.0     0.0   \n",
       "\n",
       "        Loss98  Loss99  Loss100  \n",
       "1         0.00     0.0   834.72  \n",
       "2         0.00     0.0     0.00  \n",
       "3         0.00     0.0     0.00  \n",
       "4         0.00     0.0     0.00  \n",
       "5         0.00     0.0     0.00  \n",
       "...        ...     ...      ...  \n",
       "9996      0.00     0.0     0.00  \n",
       "9997      0.00     0.0     0.00  \n",
       "9998      0.00     0.0     0.00  \n",
       "9999   1103.49     0.0   834.72  \n",
       "10000     0.00     0.0     0.00  \n",
       "\n",
       "[10000 rows x 100 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simu_loss = compute_loss(myportfolio, default_df, N_entities)\n",
    "simu_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rolling Mean, Stdv and Portfolio Loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_simu_df(loss, confidence, n_simu):\n",
    "    loss_dataframe = pd.DataFrame(loss.sum(axis=1))\n",
    "    loss_dataframe.columns = ['Loss']\n",
    "    loss_dataframe['Rolling_mean'] = loss_dataframe.expanding().mean()\n",
    "    loss_dataframe['Rolling Stdev'] = loss_dataframe['Loss'].expanding().std()\n",
    "    a = norm.ppf(confidence)\n",
    "    N = np.sqrt(np.array(range (1,n_simu + 1)))\n",
    "    loss_dataframe['Born_inf'] = loss_dataframe['Rolling_mean'] - a*loss_dataframe['Rolling Stdev']/N\n",
    "    loss_dataframe['Born_sup'] = loss_dataframe['Rolling_mean'] + a*loss_dataframe['Rolling Stdev']/N\n",
    "    loss_dataframe['Error'] = loss_dataframe['Born_sup'] - loss_dataframe['Born_inf']\n",
    "    return loss_dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Loss</th>\n",
       "      <th>Rolling_mean</th>\n",
       "      <th>Rolling Stdev</th>\n",
       "      <th>Born_inf</th>\n",
       "      <th>Born_sup</th>\n",
       "      <th>Error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>11640.09</td>\n",
       "      <td>11640.090000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>572.46</td>\n",
       "      <td>6106.275000</td>\n",
       "      <td>7825.996225</td>\n",
       "      <td>-6767.303761</td>\n",
       "      <td>18979.853761</td>\n",
       "      <td>25747.157521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1325.52</td>\n",
       "      <td>4512.690000</td>\n",
       "      <td>6183.983175</td>\n",
       "      <td>-3793.126463</td>\n",
       "      <td>12818.506463</td>\n",
       "      <td>16611.632926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.00</td>\n",
       "      <td>3384.517500</td>\n",
       "      <td>5530.418131</td>\n",
       "      <td>-3048.320730</td>\n",
       "      <td>9817.355730</td>\n",
       "      <td>12865.676461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>968.49</td>\n",
       "      <td>2901.312000</td>\n",
       "      <td>4909.845344</td>\n",
       "      <td>-2206.765390</td>\n",
       "      <td>8009.389390</td>\n",
       "      <td>10216.154779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9996</td>\n",
       "      <td>6253.04</td>\n",
       "      <td>3699.971189</td>\n",
       "      <td>3384.887453</td>\n",
       "      <td>3621.211179</td>\n",
       "      <td>3778.731200</td>\n",
       "      <td>157.520022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9997</td>\n",
       "      <td>0.00</td>\n",
       "      <td>3699.601081</td>\n",
       "      <td>3384.920421</td>\n",
       "      <td>3620.844243</td>\n",
       "      <td>3778.357920</td>\n",
       "      <td>157.513677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9998</td>\n",
       "      <td>766.80</td>\n",
       "      <td>3699.307743</td>\n",
       "      <td>3384.878203</td>\n",
       "      <td>3620.555825</td>\n",
       "      <td>3778.059660</td>\n",
       "      <td>157.503835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9999</td>\n",
       "      <td>15281.14</td>\n",
       "      <td>3700.466042</td>\n",
       "      <td>3386.690081</td>\n",
       "      <td>3621.675909</td>\n",
       "      <td>3779.256174</td>\n",
       "      <td>157.580265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10000</td>\n",
       "      <td>727.47</td>\n",
       "      <td>3700.168742</td>\n",
       "      <td>3386.651221</td>\n",
       "      <td>3621.383453</td>\n",
       "      <td>3778.954031</td>\n",
       "      <td>157.570577</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Loss  Rolling_mean  Rolling Stdev     Born_inf      Born_sup  \\\n",
       "1      11640.09  11640.090000            NaN          NaN           NaN   \n",
       "2        572.46   6106.275000    7825.996225 -6767.303761  18979.853761   \n",
       "3       1325.52   4512.690000    6183.983175 -3793.126463  12818.506463   \n",
       "4          0.00   3384.517500    5530.418131 -3048.320730   9817.355730   \n",
       "5        968.49   2901.312000    4909.845344 -2206.765390   8009.389390   \n",
       "...         ...           ...            ...          ...           ...   \n",
       "9996    6253.04   3699.971189    3384.887453  3621.211179   3778.731200   \n",
       "9997       0.00   3699.601081    3384.920421  3620.844243   3778.357920   \n",
       "9998     766.80   3699.307743    3384.878203  3620.555825   3778.059660   \n",
       "9999   15281.14   3700.466042    3386.690081  3621.675909   3779.256174   \n",
       "10000    727.47   3700.168742    3386.651221  3621.383453   3778.954031   \n",
       "\n",
       "              Error  \n",
       "1               NaN  \n",
       "2      25747.157521  \n",
       "3      16611.632926  \n",
       "4      12865.676461  \n",
       "5      10216.154779  \n",
       "...             ...  \n",
       "9996     157.520022  \n",
       "9997     157.513677  \n",
       "9998     157.503835  \n",
       "9999     157.580265  \n",
       "10000    157.570577  \n",
       "\n",
       "[10000 rows x 6 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss_dataframe = loss_simu_df(simu_loss, 0.99, 10000)\n",
    "loss_dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_loss(rolling_mean, rolling_stdv, born_inf, born_sup):\n",
    "    fig, (ax1, ax2) = plt.subplots(2, figsize=(14,10))\n",
    "    fig.suptitle('Convergence perte moyenne portefeuille')\n",
    "    ax1.plot(rolling_mean, label='Rolling Mean', color='orange')\n",
    "    ax1.plot(born_inf, label='Born_inf', color='green')\n",
    "    ax1.plot(born_sup, label='Born_sup', color='red')\n",
    "    ax2.plot(rolling_stdv, label='Rolling Stdv', color='blue')\n",
    "    #plt.ylabel('Loss', fontsize=16)\n",
    "    plt.xlabel('Simulation')\n",
    "    ax1.legend()\n",
    "    ax2.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss(loss_dataframe['Rolling_mean'], loss_dataframe['Rolling Stdev'], loss_dataframe['Born_inf'], loss_dataframe['Born_sup'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Value at Risk : VaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def var(data, confidence):\n",
    "    return data.quantile(confidence)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "confidence = data_2['IC'][0]\n",
    "VaR = var(loss_dataframe['Loss'], confidence)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value at Risk : 15438.49\n"
     ]
    }
   ],
   "source": [
    "print(\"Value at Risk : {:.2f}\".format(VaR))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Loss for all our simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Loss : 3700.17\n"
     ]
    }
   ],
   "source": [
    "mean_loss = loss_dataframe['Loss'].mean()\n",
    "print(\"Mean Loss : {:.2f}\".format(mean_loss))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute Portfolio Expected Loss "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_loss(maturity, data):\n",
    "    data['Expected Loss'] = data['Exposure']*data['LGD']*data[maturity]\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exposure</th>\n",
       "      <th>Rating</th>\n",
       "      <th>LGD</th>\n",
       "      <th>Sector</th>\n",
       "      <th>1Y</th>\n",
       "      <th>3Y</th>\n",
       "      <th>5Y</th>\n",
       "      <th>Correlation</th>\n",
       "      <th>Barrier1Y</th>\n",
       "      <th>Expected Loss</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1894</td>\n",
       "      <td>1</td>\n",
       "      <td>0.59</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0015</td>\n",
       "      <td>0.00225</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-3.090232</td>\n",
       "      <td>1.11746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1095</td>\n",
       "      <td>4</td>\n",
       "      <td>0.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.0240</td>\n",
       "      <td>0.03600</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-2.144411</td>\n",
       "      <td>7.70880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1627</td>\n",
       "      <td>6</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.0540</td>\n",
       "      <td>0.08100</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-1.799118</td>\n",
       "      <td>40.41468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1914</td>\n",
       "      <td>10</td>\n",
       "      <td>0.57</td>\n",
       "      <td>3</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-1.281552</td>\n",
       "      <td>109.09800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>1662</td>\n",
       "      <td>8</td>\n",
       "      <td>0.46</td>\n",
       "      <td>4</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.0960</td>\n",
       "      <td>0.14400</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-1.522036</td>\n",
       "      <td>48.92928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>1841</td>\n",
       "      <td>3</td>\n",
       "      <td>0.52</td>\n",
       "      <td>2</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.0135</td>\n",
       "      <td>0.02025</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-2.365618</td>\n",
       "      <td>8.61588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>1779</td>\n",
       "      <td>2</td>\n",
       "      <td>0.40</td>\n",
       "      <td>4</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.0060</td>\n",
       "      <td>0.00900</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-2.652070</td>\n",
       "      <td>2.84640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>1809</td>\n",
       "      <td>10</td>\n",
       "      <td>0.61</td>\n",
       "      <td>1</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-1.281552</td>\n",
       "      <td>110.34900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>1737</td>\n",
       "      <td>7</td>\n",
       "      <td>0.46</td>\n",
       "      <td>3</td>\n",
       "      <td>0.049</td>\n",
       "      <td>0.0735</td>\n",
       "      <td>0.11025</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-1.654628</td>\n",
       "      <td>39.15198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>100</td>\n",
       "      <td>1776</td>\n",
       "      <td>10</td>\n",
       "      <td>0.47</td>\n",
       "      <td>2</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-1.281552</td>\n",
       "      <td>83.47200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Exposure  Rating   LGD  Sector     1Y      3Y       5Y  Correlation  \\\n",
       "Id                                                                         \n",
       "1        1894       1  0.59       2  0.001  0.0015  0.00225         0.32   \n",
       "2        1095       4  0.44       1  0.016  0.0240  0.03600         0.23   \n",
       "3        1627       6  0.69       1  0.036  0.0540  0.08100         0.23   \n",
       "4        1914      10  0.57       3  0.100  0.1500  0.22500         0.15   \n",
       "5        1662       8  0.46       4  0.064  0.0960  0.14400         0.18   \n",
       "..        ...     ...   ...     ...    ...     ...      ...          ...   \n",
       "96       1841       3  0.52       2  0.009  0.0135  0.02025         0.32   \n",
       "97       1779       2  0.40       4  0.004  0.0060  0.00900         0.18   \n",
       "98       1809      10  0.61       1  0.100  0.1500  0.22500         0.23   \n",
       "99       1737       7  0.46       3  0.049  0.0735  0.11025         0.15   \n",
       "100      1776      10  0.47       2  0.100  0.1500  0.22500         0.32   \n",
       "\n",
       "     Barrier1Y  Expected Loss  \n",
       "Id                             \n",
       "1    -3.090232        1.11746  \n",
       "2    -2.144411        7.70880  \n",
       "3    -1.799118       40.41468  \n",
       "4    -1.281552      109.09800  \n",
       "5    -1.522036       48.92928  \n",
       "..         ...            ...  \n",
       "96   -2.365618        8.61588  \n",
       "97   -2.652070        2.84640  \n",
       "98   -1.281552      110.34900  \n",
       "99   -1.654628       39.15198  \n",
       "100  -1.281552       83.47200  \n",
       "\n",
       "[100 rows x 10 columns]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myportfolio = expected_loss('1Y', myportfolio)\n",
    "myportfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def E_Loss(portfolio):\n",
    "    EL = portfolio['Expected Loss'].sum()\n",
    "    return EL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected Loss : 3683.22\n"
     ]
    }
   ],
   "source": [
    "EL = E_Loss(myportfolio)\n",
    "print(\"Expected Loss : {:.2f}\".format(EL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expected Shortfall : ES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_shortfall(loss, value_at_risk):\n",
    "    ES = loss['Loss'][loss['Loss'] > value_at_risk ].mean()\n",
    "    return ES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of values greater than the VaR : 100.00\n",
      "Expected Shortfall : 18055.89\n"
     ]
    }
   ],
   "source": [
    "##Number of loss values greater than the VaR and compute ES\n",
    "number = loss_dataframe['Loss'][loss_dataframe['Loss'] > VaR].count()\n",
    "ES = expected_shortfall(loss_dataframe, VaR)\n",
    "print(\"Number of values greater than the VaR : {:.2f}\".format(number))\n",
    "print(\"Expected Shortfall : {:.2f}\".format(ES))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All indicators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_indicators(loss, confidence, portfolio):\n",
    "    VaR = var(loss['Loss'], confidence)\n",
    "    mean_loss = loss['Loss'].mean()\n",
    "    EL = E_Loss(portfolio)\n",
    "    expected_shortfall(loss, VaR)\n",
    "    UL = VaR - EL\n",
    "    porfolio_indicators = pd.DataFrame({'VaR': VaR, 'Average Loss' : mean_loss, 'Expected Loss': EL, 'Unexpected Loss': UL, 'Expected Shortfall':ES }, index = ['value'])\n",
    "    return porfolio_indicators "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VaR</th>\n",
       "      <th>Average Loss</th>\n",
       "      <th>Expected Loss</th>\n",
       "      <th>Unexpected Loss</th>\n",
       "      <th>Expected Shortfall</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>value</td>\n",
       "      <td>15438.4945</td>\n",
       "      <td>3700.168742</td>\n",
       "      <td>3683.2199</td>\n",
       "      <td>11755.2746</td>\n",
       "      <td>18055.8895</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              VaR  Average Loss  Expected Loss  Unexpected Loss  \\\n",
       "value  15438.4945   3700.168742      3683.2199       11755.2746   \n",
       "\n",
       "       Expected Shortfall  \n",
       "value          18055.8895  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "porfolio_indicators = compute_indicators(loss_dataframe, data_2['IC'][0], myportfolio)\n",
    "porfolio_indicators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Indicators analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0.8: value    5917.516\n",
       " Name: VaR, dtype: float64, 0.85: value    6888.548\n",
       " Name: VaR, dtype: float64, 0.9: value    8181.246\n",
       " Name: VaR, dtype: float64, 0.95: value    10339.778\n",
       " Name: VaR, dtype: float64, 0.97: value    12156.6875\n",
       " Name: VaR, dtype: float64, 0.99: value    15438.4945\n",
       " Name: VaR, dtype: float64}"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_list = [0.8, 0.85, 0.90, 0.95, 0.97, 0.99]\n",
    "dic = {}\n",
    "for i in c_list:\n",
    "    dic[i] = compute_indicators(loss_dataframe, i, myportfolio)['VaR']\n",
    "dic \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0.80</th>\n",
       "      <th>0.85</th>\n",
       "      <th>0.90</th>\n",
       "      <th>0.95</th>\n",
       "      <th>0.97</th>\n",
       "      <th>0.99</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>value</td>\n",
       "      <td>5917.516</td>\n",
       "      <td>6888.548</td>\n",
       "      <td>8181.246</td>\n",
       "      <td>10339.778</td>\n",
       "      <td>12156.6875</td>\n",
       "      <td>15438.4945</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0.80      0.85      0.90       0.95        0.97        0.99\n",
       "value  5917.516  6888.548  8181.246  10339.778  12156.6875  15438.4945"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dd = pd.DataFrame(dic)\n",
    "dd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### It can be seen above that when the chosen confidence level reaches high levels, the VaR increases very quickly. \n",
    "### This shows the importance of the choice of the confidence level in the calculation of the capital requirement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CDO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cdo(loss, portfolio, strike, size):\n",
    "    df = pd.DataFrame(loss['Loss'])\n",
    "    total = portfolio['Exposure'].sum()\n",
    "    df['Loss %'] = (df['Loss']/total)*100\n",
    "    df['Tranche'] = df['Loss %'] - 7\n",
    "    df.loc[df['Tranche'] < 0, 'Tranche'] = 0\n",
    "    df.loc[df['Tranche'] > size, 'Tranche'] = size\n",
    "    df['Tranche 100%'] = (df['Tranche']/size)*100\n",
    "    percent = df['Tranche 100%'].mean()/100\n",
    "    price = (percent * size * total)/100\n",
    "    return price, df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "price, dataframe = compute_cdo(loss_dataframe, myportfolio, 7, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "89.29195500000003"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# II. IPYWIDGET INTERACTIVE PLOTTING"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual, Layout\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import FloatSlider, IntSlider\n",
    "from IPython.display import display "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Main function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b0f6bf3becf94e01912c67b4e0d5f30c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='confidence', options=(0.8, 0.85, 0.9, 0.95, 0.97, 0.99), value=0.8…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.display_result(confidence, maturity, global_corr, strike, size, n_simu)>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def display_result(confidence, maturity, global_corr, strike, size, n_simu):\n",
    "    ###Arguments\n",
    "    \n",
    "    #confidence : interval de confiance\n",
    "    #maturity : 1Y, 3Y ou 5Y\n",
    "    #global_corr : corrélation\n",
    "    \n",
    "    \n",
    "    #Compute portfolio barrier\n",
    "    barrier = compute_barrier(merged_portfolio, maturity)\n",
    "    #compute the expected loss column and return portfolio\n",
    "    portfolio = expected_loss(maturity, barrier)\n",
    "    \n",
    "    #generate monte carlo simulations\n",
    "    simulations = generate(n_simu, N_entities, N_sectors)\n",
    "    #Compute Z_i, our default model : MG2F\n",
    "    Z_i = compute_Z(simulations, N_entities, n_simu, global_corr)\n",
    "    #Get the default dataframe with 1 and 0 based on whether we're default or not\n",
    "    D_i = whendefault(portfolio,Z_i, N_entities, n_simu, maturity)\n",
    "    #Compute our assets losses for the n_simu simulations\n",
    "    Loss_i = compute_loss(portfolio, D_i, N_entities)\n",
    "    #Get the Portfolio Losses which is a datafame composed of Loss, rolling mean & stdv, Born_inf, Born_sup\n",
    "    simu_losses = loss_simu_df(Loss_i, confidence, n_simu)\n",
    "    #Compute our porfolio indicators (Var, EL, UL, ES)\n",
    "    indicators = compute_indicators(simu_losses, confidence, portfolio)\n",
    "    #Get the price : CDO\n",
    "    price_cdo, df = compute_cdo(simu_losses, portfolio, strike, size)\n",
    "    \n",
    "    #plot rolling mean and stdv\n",
    "    plotted = plot_loss(simu_losses['Rolling_mean'], simu_losses['Rolling Stdev'], simu_losses['Born_inf'], simu_losses['Born_sup'])\n",
    "    \n",
    "    print('--------------------------------------------------------')\n",
    "    \n",
    "    print(' ')\n",
    "    print('\\033[1m' + 'THIS IS YOUR PORTFOLIO')\n",
    "    \n",
    "    display(portfolio.head(10))\n",
    "    \n",
    "    print('\\033[94m')\n",
    "    \n",
    "    print('\\033[1m' + 'PORTFOLIO INDICATORS')\n",
    "    \n",
    "    display(indicators)\n",
    "    \n",
    "    print('\\033[92m')\n",
    "    print('--------------------------------------------------------')\n",
    "    \n",
    "    print('\\033[1m' + 'COLLATERALIZED DEBT OBLIGATION : CDO')\n",
    "    \n",
    "    print('')\n",
    "    \n",
    "    print(\"Price : {:.2f}\".format(price_cdo))\n",
    "\n",
    "    \n",
    "#Defines our arguments    \n",
    "mat = ['1Y', '3Y', '5Y'] \n",
    "c_list = [0.8, 0.85, 0.90, 0.95, 0.97, 0.99]\n",
    "nb_simu = IntSlider(min=0, max=100000, step=100)\n",
    "rho_list = FloatSlider(min=0, max=1, step=0.01)\n",
    "s_values = IntSlider(min=1, max=50, step=1)\n",
    "size_values = IntSlider(min=1, max=10, step=1)\n",
    "\n",
    "interact_manual(display_result, confidence=c_list, maturity=mat, global_corr=rho_list, strike=s_values, size=size_values, n_simu=nb_simu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All in one "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Portfolio():\n",
    "\n",
    "    def __init__(self, N_simu, N_entities, N_sectors, maturity, rho, dataframe):\n",
    "        self.N_simu = N_simu\n",
    "        self.N_entities = N_entities\n",
    "        self.N_sectors = N_sectors\n",
    "        self.maturity = maturity\n",
    "        self.rho = rho\n",
    "        self.dataframe = dataframe\n",
    "    \n",
    "    \n",
    "    def getData(self):\n",
    "        barrier = self.compute_barrier(self.dataframe)\n",
    "        myportfolio = self.expected_loss(self.maturity, barrier)\n",
    "        return myportfolio\n",
    "    \n",
    "    def getPlot(self):\n",
    "        \n",
    "        #Generate Simulations \n",
    "        mydata = self.generate_simu()\n",
    "        #Compute Z\n",
    "        default = self.compute_Z()\n",
    "        #when default\n",
    "        myportfolio = self.getData()\n",
    "        default_df = self.whendefault(myportfolio, default)\n",
    "        loss_df = self.compute_loss(myportfolio, default_df)\n",
    "        loss_plot = self.rolling_mean_stdv(loss_df)[['Rolling_mean', 'Rolling Stdev']]\n",
    "        plt_obj = loss_plot.plot()\n",
    "        plt_obj.set_ylabel(\"Perte moyenne\")\n",
    "        plt_obj.set_title(\"Evolution moyenne perte et stdv en fonction des simulations\")\n",
    "        fig = plt_obj.get_figure()\n",
    "        return fig        \n",
    "        \n",
    "    \n",
    "    def generate_simu(self):\n",
    "        #generate monte carlo simulation for X, the 100 entites and the 5 sectors\n",
    "        simulations = np.random.randn(self.N_simu, self.N_entities + self.N_sectors + 1)\n",
    "        #Convert to DataFrime\n",
    "        mydata = pd.DataFrame(simulations, index = [i for i in range(1,self.N_simu + 1)])\n",
    "        mydata.columns = ['X'] + ['X' +str(i) for i in range(1,self.N_sectors + 1)] + ['E' +str(i) for i in range(1, self.N_entities + 1)]\n",
    "        return mydata\n",
    "    \n",
    "    \n",
    "    def compute_Z(self):\n",
    "        #create the dataframe with nan values\n",
    "        default = pd.DataFrame(columns=['Z' +str(i) for i in range(1, self.N_entities + 1)], index = [i for i in range(1, self.N_simu + 1)])\n",
    "        #compute Z\n",
    "        simu_df = self.generate_simu()\n",
    "        for i in range(1,self.N_entities + 1):\n",
    "            default['Z' +str(i)] = np.sqrt(self.rho) * simu_df['X'] + np.sqrt(1 - merged_portfolio['Correlation'][i]) * simu_df['E' +str(i)] + np.sqrt(merged_portfolio['Correlation'][i]-self.rho)*simu_df['X' +str(merged_portfolio['Sector'][i])]\n",
    "        return default\n",
    "    \n",
    "    #Compute barrier\n",
    "    def compute_barrier(self,portfolio):\n",
    "        portfolio['Barrier' + self.maturity] = norm.ppf(portfolio[self.maturity])\n",
    "        return portfolio\n",
    "    \n",
    "    def whendefault(self, myportfolio,default):\n",
    "        df = pd.DataFrame(columns=['D' +str(i) for i in range(1, self.N_entities + 1)], index = [i for i in range(1, self.N_simu + 1)])\n",
    "        for i in range(1, self.N_entities + 1):\n",
    "            df['D' +str(i)] = default['Z' +str(i)].apply(lambda x: 1 if x <= myportfolio['Barrier' + self.maturity][i] else 0)\n",
    "        return df \n",
    "    \n",
    "    #compute simualtion loss dataframe\n",
    "    def compute_loss(self, myportfolio, default_df):\n",
    "        loss_df = default_df.copy()\n",
    "        loss_df.columns = ['Loss' +str(i) for i in range(1, self.N_entities + 1)]\n",
    "        for i in range(1, N_entities + 1):\n",
    "            loss_df['Loss' +str(i)] = default_df['D' +str(i)].apply(lambda x: x * myportfolio['Exposure'][i] * myportfolio['LGD'][i])\n",
    "        return loss_df \n",
    "    \n",
    "    def rolling_mean_stdv(self, loss_df):\n",
    "        loss_dataframe = pd.DataFrame(loss_df.sum(axis=1))\n",
    "        loss_dataframe.columns = ['Loss']\n",
    "        loss_dataframe['Rolling_mean'] = loss_dataframe.expanding().mean()\n",
    "        loss_dataframe['Rolling Stdev'] = loss_dataframe['Loss'].expanding().std()\n",
    "        return loss_dataframe\n",
    "    \n",
    "\n",
    "    \n",
    "    def expected_loss(self, maturity, data):\n",
    "        data['Expected Loss'] = data['Exposure']*data['LGD']*data[maturity]\n",
    "        return data\n",
    "      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio_output = Portfolio(N_simu, N_entities, N_sectors, '1Y', 0.11, merged_portfolio).getData()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exposure</th>\n",
       "      <th>Rating</th>\n",
       "      <th>LGD</th>\n",
       "      <th>Sector</th>\n",
       "      <th>1Y</th>\n",
       "      <th>3Y</th>\n",
       "      <th>5Y</th>\n",
       "      <th>Correlation</th>\n",
       "      <th>Barrier1Y</th>\n",
       "      <th>Expected Loss</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1894</td>\n",
       "      <td>1</td>\n",
       "      <td>0.59</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0015</td>\n",
       "      <td>0.00225</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-3.090232</td>\n",
       "      <td>1.11746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1095</td>\n",
       "      <td>4</td>\n",
       "      <td>0.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.0240</td>\n",
       "      <td>0.03600</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-2.144411</td>\n",
       "      <td>7.70880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1627</td>\n",
       "      <td>6</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1</td>\n",
       "      <td>0.036</td>\n",
       "      <td>0.0540</td>\n",
       "      <td>0.08100</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-1.799118</td>\n",
       "      <td>40.41468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1914</td>\n",
       "      <td>10</td>\n",
       "      <td>0.57</td>\n",
       "      <td>3</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-1.281552</td>\n",
       "      <td>109.09800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>1662</td>\n",
       "      <td>8</td>\n",
       "      <td>0.46</td>\n",
       "      <td>4</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.0960</td>\n",
       "      <td>0.14400</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-1.522036</td>\n",
       "      <td>48.92928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>1841</td>\n",
       "      <td>3</td>\n",
       "      <td>0.52</td>\n",
       "      <td>2</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.0135</td>\n",
       "      <td>0.02025</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-2.365618</td>\n",
       "      <td>8.61588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>1779</td>\n",
       "      <td>2</td>\n",
       "      <td>0.40</td>\n",
       "      <td>4</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.0060</td>\n",
       "      <td>0.00900</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-2.652070</td>\n",
       "      <td>2.84640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>1809</td>\n",
       "      <td>10</td>\n",
       "      <td>0.61</td>\n",
       "      <td>1</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-1.281552</td>\n",
       "      <td>110.34900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>1737</td>\n",
       "      <td>7</td>\n",
       "      <td>0.46</td>\n",
       "      <td>3</td>\n",
       "      <td>0.049</td>\n",
       "      <td>0.0735</td>\n",
       "      <td>0.11025</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-1.654628</td>\n",
       "      <td>39.15198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>100</td>\n",
       "      <td>1776</td>\n",
       "      <td>10</td>\n",
       "      <td>0.47</td>\n",
       "      <td>2</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1500</td>\n",
       "      <td>0.22500</td>\n",
       "      <td>0.32</td>\n",
       "      <td>-1.281552</td>\n",
       "      <td>83.47200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Exposure  Rating   LGD  Sector     1Y      3Y       5Y  Correlation  \\\n",
       "Id                                                                         \n",
       "1        1894       1  0.59       2  0.001  0.0015  0.00225         0.32   \n",
       "2        1095       4  0.44       1  0.016  0.0240  0.03600         0.23   \n",
       "3        1627       6  0.69       1  0.036  0.0540  0.08100         0.23   \n",
       "4        1914      10  0.57       3  0.100  0.1500  0.22500         0.15   \n",
       "5        1662       8  0.46       4  0.064  0.0960  0.14400         0.18   \n",
       "..        ...     ...   ...     ...    ...     ...      ...          ...   \n",
       "96       1841       3  0.52       2  0.009  0.0135  0.02025         0.32   \n",
       "97       1779       2  0.40       4  0.004  0.0060  0.00900         0.18   \n",
       "98       1809      10  0.61       1  0.100  0.1500  0.22500         0.23   \n",
       "99       1737       7  0.46       3  0.049  0.0735  0.11025         0.15   \n",
       "100      1776      10  0.47       2  0.100  0.1500  0.22500         0.32   \n",
       "\n",
       "     Barrier1Y  Expected Loss  \n",
       "Id                             \n",
       "1    -3.090232        1.11746  \n",
       "2    -2.144411        7.70880  \n",
       "3    -1.799118       40.41468  \n",
       "4    -1.281552      109.09800  \n",
       "5    -1.522036       48.92928  \n",
       "..         ...            ...  \n",
       "96   -2.365618        8.61588  \n",
       "97   -2.652070        2.84640  \n",
       "98   -1.281552      110.34900  \n",
       "99   -1.654628       39.15198  \n",
       "100  -1.281552       83.47200  \n",
       "\n",
       "[100 rows x 10 columns]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "portfolio_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot = portfolio_output = Portfolio(N_simu, N_entities, N_sectors, '1Y', 0.11, merged_portfolio).getPlot()\n",
    "plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}