{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#In-this-notebook\" data-toc-modified-id=\"In-this-notebook-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>In this notebook</a></span></li><li><span><a href=\"#PDF,-CDF-and-Quantile-functions\" data-toc-modified-id=\"PDF,-CDF-and-Quantile-functions-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>PDF, CDF and Quantile functions</a></span><ul class=\"toc-item\"><li><span><a href=\"#Standard-Gaussian\" data-toc-modified-id=\"Standard-Gaussian-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Standard Gaussian</a></span></li><li><span><a href=\"#Other-examples-of-continuous-distributions\" data-toc-modified-id=\"Other-examples-of-continuous-distributions-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Other examples of continuous distributions</a></span></li><li><span><a href=\"#Examples-of-discrete-distributions\" data-toc-modified-id=\"Examples-of-discrete-distributions-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>Examples of discrete distributions</a></span></li></ul></li><li><span><a href=\"#Calculating-V@R,-ES-using-quantiles\" data-toc-modified-id=\"Calculating-V@R,-ES-using-quantiles-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Calculating V@R, ES using quantiles</a></span><ul class=\"toc-item\"><li><span><a href=\"#Value-at-risk\" data-toc-modified-id=\"Value-at-risk-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Value at risk</a></span></li><li><span><a href=\"#Expected-shortfall\" data-toc-modified-id=\"Expected-shortfall-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Expected shortfall</a></span></li></ul></li><li><span><a href=\"#Monte-Carlo-approximations\" data-toc-modified-id=\"Monte-Carlo-approximations-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Monte Carlo approximations</a></span></li><li><span><a href=\"#Exercises\" data-toc-modified-id=\"Exercises-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Exercises</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Risk measures\n",
    "**Camilo A. Garcia Trillos - 2020**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## In this notebook\n",
    "\n",
    "- we learn some probability distributions available in scipy.stats.\n",
    "- we use the associated functions to calculate V@R and ES\n",
    "- we introduce a Monte Carlo estimator for both V@R and ES"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Some distributions do not have easy formulas for their value at risk or expeted shortfall. We introduce here some functions and procedures in Python to approximate their value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We start by importing the modules we use in this notebook. The package scipy.stats contains some statistical distributions and tests. We will use some of the functions on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import default_rng\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as st"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## PDF, CDF and Quantile functions\n",
    "\n",
    "It is possible to calculate directly the PDF, CDF and quantile function for several distributions in Pytho, thanks to the scipy.stats library. This is achieved with the following general structure: \n",
    "\n",
    "- PDF: *st.[name distribution].pdf(probability, parameters)*\n",
    "- CDF: *st.[name distribution].cdf(probability, parameters)*\n",
    "- Quantile function: *st.[name distribution].ppf(probability, parameters)*\n",
    "\n",
    "\n",
    "\n",
    "Let us illustrate with some examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Standard Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'pdf')"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 726
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting the pdf\n",
    "\n",
    "x = np.linspace(-3,3,50) #Take 50 equally spaced points between -3 and 3\n",
    "y = st.norm.pdf(x) # calculate the pdf for each one \n",
    "\n",
    "plt.plot(x, y) # plot\n",
    "plt.title('PDF standard Gaussian')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We recover the familiar bell-shaped pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'cdf')"
      ]
     },
     "execution_count": 3,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 720
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting the cdf\n",
    "\n",
    "x = np.linspace(-3,3,50) #Take 50 equally spaced points between -3 and 3\n",
    "y = st.norm.cdf(x) # calculate the pdf for each one \n",
    "\n",
    "plt.plot(x, y) # plot\n",
    "plt.title('CDF standard Gaussian')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('cdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The plot illustrates the properties of the cdf: non-decreasing, with limits and $-\\infty$ and $\\infty$ equal to 0 and 1 respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'x')"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 719
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting the quantile function\n",
    "\n",
    "x = np.linspace(0,1,100) #Take 100 equally spaced points between 0 and 1\n",
    "y = st.norm.ppf(x) # calculate the pdf for each one \n",
    "\n",
    "plt.plot(x, y) # plot\n",
    "plt.title('Quantile function -  standard Gaussian')\n",
    "plt.xlabel('probability')\n",
    "plt.ylabel('x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Note how this is the reflection of the CDF plot around the x=y line.\n",
    "\n",
    "Some numbers that appear commonly are associated to the quantile at levels 0.95 and 0.99 for the Gaussian distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantile at level 0.95:  1.6448536269514722\n",
      "Quantile at level 0.99:  2.3263478740408408\n"
     ]
    }
   ],
   "source": [
    "# Standard Gaussian, quantile 0.99\n",
    "\n",
    "print('Quantile at level 0.95: ', st.norm.ppf(0.95))\n",
    "print('Quantile at level 0.99: ', st.norm.ppf(0.99))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Other examples of continuous distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.6526957480816815\n",
      "5.6526957480816815\n"
     ]
    }
   ],
   "source": [
    "#Gaussian with mean 1 and variance 4, quantile 0.99\n",
    "print(st.norm.ppf(0.99,1,2))\n",
    "\n",
    "#Due to the specific structure of Gaussian variables, this coincides with a rescaling of the standard one:\n",
    "print(st.norm.ppf(0.99)*2+1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'pdf')"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 726
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The pdf of a standard - t with 4 degrees of freedom.\n",
    "\n",
    "\n",
    "x = np.linspace(-5,5,50) #Take 50 equally spaced points between -3 and 3\n",
    "y = st.t.pdf(x,4) # calculate the pdf for each one \n",
    "\n",
    "plt.plot(x, y) # plot\n",
    "plt.title('PDF - t with 4 d. of f.')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.7469473879811366"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A t-distribution with 4 degrees of freedom and standard form, quantile 0.99\n",
    "\n",
    "st.t.ppf(0.99,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6437211935036444"
      ]
     },
     "execution_count": 9,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A chi-square distribution with 4 degrees of freedom\n",
    "\n",
    "st.chi.ppf(0.99,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "There are many more distributions tahn the ones above. Have a look at the help to know more."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Examples of discrete distributions\n",
    "\n",
    "In the case of discrete distributions, there is no pdf function. Instead, we have a probabity function ($p(x):=\\mathbb P(X=x)$) which is calculated in the scipy.stats package using the following structure:\n",
    "\n",
    "- st.[name distribution].pdf(probability, parameters)\n",
    "\n",
    "The CDF and quantile are calculated as for the continuous case.\n",
    "\n",
    "Let us see one example with the Poisson distribution. Recall that if $X$ is distributed Poisson with parameter $\\mu$,\n",
    "$$P[X=n] = e^{-\\mu} \\frac{\\mu^n}{n!} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'probability')"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 733
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting probability\n",
    "\n",
    "x = np.arange(15)\n",
    "y = st.poisson.pmf(x,5)\n",
    "\n",
    "plt.plot(x, y,'bo') # plot\n",
    "plt.title('Probability Poisson mu=5')\n",
    "plt.vlines(x, 0, y, colors='b', lw=1, alpha=0.2)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('probability')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 720
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting cdf\n",
    "\n",
    "x = np.arange(15)\n",
    "y = st.poisson.cdf(x,5)\n",
    "\n",
    "plt.step(x, y, where='post') # the post label assumes a right continuous function\n",
    "plt.plot(x, y, 'bo') # plot\n",
    "plt.title('CDF Poisson mu=5')\n",
    "#plt.vlines(x, 0, y, colors='b', lw=1, alpha=0.2)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('probability');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 717
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting quantile\n",
    "\n",
    "x = st.poisson.cdf(np.arange(15),5) #Take the values we plotted before\n",
    "y = st.poisson.ppf(x,5)\n",
    "\n",
    "plt.step(x, y, where='pre') # the pre label assumes a left continuous function\n",
    "plt.plot(x, y, 'bo') # plot\n",
    "plt.title('Quantile function Poisson mu=5')\n",
    "#plt.vlines(x, 0, y, colors='b', lw=1, alpha=0.2)\n",
    "plt.xlabel('probability')\n",
    "plt.ylabel('quantile');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Calculating V@R, ES using quantiles\n",
    "\n",
    "Let us implement two functions that receive a (static) instance of a probability distribution from scipy.stats, and return V@R and ES.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Value at risk\n",
    "\n",
    "Taking $X$ to be a random variable denoting, for example, profit and losses, we can easily calculate Value at Risk whenever $X$ is distributed following one of the distributions in scipy.stats, by using the quantile function.  \n",
    "\n",
    "We can show that (see lecture notes)\n",
    "$$ \\mathrm{V@R}^\\alpha(X) = -q_{X}(1-\\alpha+ \\epsilon \\mathbb 1_{ F_X(q_X(1-\\alpha)) = 1-\\alpha  }) ,$$\n",
    "for any $\\epsilon\\in (0,P[X=q_X(1-\\alpha)])$ with the convention that $\\epsilon = 0$ if this set is empty.\n",
    "Note that in the case of a continuous distribution we get\n",
    "$$\\mathrm{V@R}^\\alpha(X) = -q_{X}(1-\\alpha).$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def varisk(dist, alpha):\n",
    "    \n",
    "    if alpha<=0 or alpha>=1:\n",
    "        raise ValueError('Alpha is outside of valid interval')\n",
    "    \n",
    "    x_aux = dist.ppf(1-alpha)\n",
    "    \n",
    "    try:  #check if calling the function pmf raises an error\n",
    "        dist.pmf(0)\n",
    "    except:  # if an error, the distribution is continuous because there is no prob. mass function\n",
    "        return -x_aux   \n",
    "    #Otherwise, the distribution is discrete\n",
    "    if dist.cdf(x_aux)==1-alpha:\n",
    "        return -1.*dist.ppf( 1-alpha+dist.pmf(x_aux)*alpha )\n",
    "    return -x_aux\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us see some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6526957480816815\n",
      "3.6526957480816815\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Value at risk at level 0.99 for a Gaussian with mean 1 and variance 4\n",
    "print(varisk(st.norm(1,2), 0.99))\n",
    "\n",
    "#The same from an exact formula (see lecture notes):\n",
    "print( 2*st.norm.ppf(0.99,0,1)-1  )\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We got the value we were expecting. Let us now check the case of a bernoulli random variable with $P[X=1]=0.75$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V@R level 0.99 -0.0\n",
      "V@R level 0.75 -1.0\n",
      "V@R level 0.60 -1.0\n"
     ]
    }
   ],
   "source": [
    "print('V@R level 0.99',varisk(st.bernoulli(0.75), 0.99))\n",
    "print('V@R level 0.75',varisk(st.bernoulli(0.75), 0.75))\n",
    "print('V@R level 0.60',varisk(st.bernoulli(0.75), 0.60))\n",
    "      \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Expected shortfall\n",
    "\n",
    "Recall (see the lecture notes) that\n",
    "\n",
    "$$\\begin{split} \n",
    "\\mathrm{ES}^\\alpha & = \\frac{1}{1-\\alpha} \\int_{\\alpha}^1 \\mathrm{V@R}^u(X)\\mathrm d u \\\\\n",
    "& =  \\frac  1 {1-\\alpha} \\left\\{ - \\mathbb{E}[X \\mathbb{1}_{X <-\\mathrm{V@R}^\\alpha(X)}] + (\\tilde \\alpha-\\alpha) \\mathrm{V@R}^\\alpha(X) \\right\\}\n",
    "\\end{split}$$\n",
    "\n",
    "where $\\tilde \\alpha:= F_{-X}(\\mathrm{V@R}^\\alpha(X)) = 1-F_{X}(-\\mathrm{V@R}^\\alpha(X)) + P[X = -\\mathrm{V@R}^\\alpha(X)]$.\n",
    "\n",
    "\n",
    "We are going to use the method 'expect' associated to a given distribution in scipy.stats. Look at the help of this function to understand more, but here are two examples of use:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of a standard Gaussian: 0.0\n",
      "Second moment of a standard Gaussian:  1.000000000000001\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of X in the interval [0,\\infty): 0.39894228040143215\n"
     ]
    }
   ],
   "source": [
    "# Example for expect\n",
    "\n",
    "print('Expected value of a standard Gaussian:', st.norm(0,1).expect(lambda x: x)) \n",
    "print('Second moment of a standard Gaussian: ', st.norm(0,1).expect(lambda x: x**2)) \n",
    "print('Expected value of X in the interval [0,\\infty):',st.norm(0,1).expect(lambda x: x, lb =0)) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can use this available function to define our own function to calculate expected shortfall."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def es(dist,alpha):\n",
    "        \n",
    "    var_alpha = varisk(dist,alpha)\n",
    "    x_aux = (-1*dist.expect(func = lambda x: x, ub = -var_alpha))/(1-alpha)\n",
    "    \n",
    "    \n",
    "    try:  #check if calling the function pmf raises an error\n",
    "        dist.pmf(0)\n",
    "    except:  # if an error, the distribution is continuous because there is no prob. mass function\n",
    "        return x_aux\n",
    "    \n",
    "    p_varalpha = dist.pmf(-1*var_alpha)\n",
    "    \n",
    "    alpha_tilde = 1-dist.cdf(-1*var_alpha) + p_varalpha\n",
    "    return x_aux + (alpha_tilde-alpha-p_varalpha)*var_alpha/(1-alpha)\n",
    "     \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.330428440691598\n",
      "4.330428440691612\n"
     ]
    }
   ],
   "source": [
    "# Expected shortfall at level 0.99 for a Gaussian with mean 1 and variance 4\n",
    "alpha = 0.99\n",
    "print(es(st.norm(1,2), alpha))\n",
    "\n",
    "#The same from an exact formula (see lecture notes):\n",
    "print( -1 + 2*( st.norm(0,1).pdf( st.norm(0,1).ppf(alpha))/(1-alpha)  ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "As can be seen, there is a small difference due to the approximation error in the function \"expect\", but the approximation is very good.\n",
    "\n",
    "Let us compare both value at risk and expected shortfall for different values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 719
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_vec = np.arange(0.01,1,0.03)\n",
    "test_dist = st.norm(0,1)\n",
    "plt.plot(alpha_vec, [varisk(test_dist,i) for i in alpha_vec], label='V@R')\n",
    "plt.plot(alpha_vec, [es(test_dist,i) for i in alpha_vec], label='ES')\n",
    "plt.legend()\n",
    "plt.title('V@R and ES for standard Gaussian')\n",
    "plt.xlabel('Probability')\n",
    "plt.ylabel('Value');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can verify visually several properties:\n",
    "- Expected shortfall is always larger or equal than value at risk\n",
    "- Expected shortfall tends to $-E[X]$ when $\\alpha\\downarrow 0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us now check the case of a Bernoulli random variable with $P[X=1]=0.75$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ES level 0.99 0.0\n",
      "ES level 0.60 -0.3750000000000002\n"
     ]
    }
   ],
   "source": [
    "print('ES level 0.99',es(st.bernoulli(0.75), 0.99))\n",
    "print('ES level 0.60',es(st.bernoulli(0.75), 0.6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 728
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_vec = np.arange(0.01,1,0.03)\n",
    "test_dist = st.bernoulli(0.75)\n",
    "plt.plot(alpha_vec, [varisk(test_dist,i) for i in alpha_vec], label='V@R')\n",
    "plt.plot(alpha_vec, [es(test_dist,i) for i in alpha_vec], label='ES')\n",
    "plt.legend()\n",
    "plt.title('V@R and ES for Bernoulli(0.75)')\n",
    "plt.xlabel('Probability')\n",
    "plt.ylabel('Value');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "This is an example that shows that expected shortfall is more regular with respect to the level. Here it is continuous in alpha while value at risk is not.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Monte Carlo approximations\n",
    "\n",
    "A Monte Carlo approximation might be useful either to replace the calculation of integrals for expected shortfall as above, or to calculate both value at risk and expected shortfall in cases where we do not have an explicit expression for the pdf. \n",
    "\n",
    "The idea is simply replace the calculation of expected shortfall or value at risk on the distribution bu that of the empirical measure coming from a large sample of the distribution.\n",
    "\n",
    "Suppose that $X_1, \\ldots, X_n$ are all i.i.d. samples of the same distribution in $\\mathbb R$. Let us also denote by $X_{(1)}, \\ldots, X_{(n)} $ this sample after ordering (i.e. $X_{(i)} \\leq X_{(j)}$ if and only if $i\\leq j$). Then we have that\n",
    "$$\\begin{split}\n",
    "\\mathrm{V@R}^\\alpha(X) & \\approx -X_{( i_\\alpha )} \\\\\n",
    "\\mathrm{ES}^\\alpha(X) &\\approx -\\frac{1}{i_\\alpha }\\sum_{k=1}^{i_\\alpha} X_{( k )}\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "where $i_\\alpha:= \\lfloor n(1-\\alpha)\\rfloor$.\n",
    "\n",
    "**Remark:** Naturally, this is not the only estimator, There are other choices of estimator that will be presented later in the lecture notes.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us define a function that calculate the approximation of value at risk and expected shortfall for any sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def var_es_sample(sample,alpha):    \n",
    "    ss=np.sort(sample)\n",
    "    ialpha = int(sample.size * (1-alpha))\n",
    "    return -ss[ialpha], -ss[:ialpha].mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can test by comparing in cases as the ones we had before. Remember the use of the random number generator.\n",
    "\n",
    "We start with the standard normal case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.6554153431984657, 4.344458055149295)"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NMC = 1000000 # Number of samples\n",
    "rng = default_rng(0)\n",
    "sample_normal = rng.normal(1,2,size=NMC)\n",
    "var_es_sample(sample_normal, 0.99)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Comparing with the values before (3.6526957480816815, 4.330428440691612), this is not a bad approximation. Note, though that we required a large sample (here, 1000000). A larger sample might be required for higher levels in VAR and ES. \n",
    "\n",
    "Also, remember that this estimator is random (this is why we had to fix the seed of the generator). You can check this by removing the seed.\n",
    "\n",
    "Let us see also the case of the Bernoulli(0.75)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, -0.0)"
      ]
     },
     "execution_count": 24,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = default_rng(123)\n",
    "sample_bernoulli=(rng.random(size = NMC)<=0.75) +0\n",
    "var_es_sample(sample_bernoulli, 0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, -0.3761125)"
      ]
     },
     "execution_count": 25,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_es_sample(sample_bernoulli, 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Again, we get close enough values to the ones defined before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Exercises\n",
    "\n",
    "1. Plot the values of value at risk for a t-distribution as a function of the number of degrees of freedom. Repeat the exercise with expected shortfall. What do you observe?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc43d6a5d90>"
      ]
     },
     "execution_count": 26,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 726
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_ref = 0.9\n",
    "var_gaussian = varisk(st.norm,alpha_ref)\n",
    "max_dof = 20\n",
    "var_gaussian = varisk(st.norm,alpha_ref)\n",
    "dof = np.arange(1,max_dof)\n",
    "var_vec = [varisk(st.t(i), alpha_ref) for i in dof]\n",
    "plt.plot(dof,var_vec)\n",
    "plt.plot(dof,np.ones(max_dof-1)*var_gaussian,'--r')\n",
    "\n",
    "\n",
    "plt.title('Value at risk at level ' + str(alpha_ref)+' for t-dist vs. degrees of freedom')\n",
    "plt.xlabel('Degrees of freedom')\n",
    "plt.ylabel('V@R')\n",
    "plt.legend(['t-distribution','Std. Gaussian'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Value at risk for values larger than 0.5 decreases as a function of the number of degrees of freedom. As expected, it seems to tend asymptotically to the value at risk of a standard Gaussian. This shows that this distribution with low degrees of freedom is riskier than a standard Gaussian from a tail point of view."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "2. Assume $X$ follows a standard Gaussian. Write a function $\\phi(\\alpha)$ such that $\\mathrm{V@R}^{\\phi(\\alpha)}(X) = \\mathrm{ES}^\\alpha(X)$. Test the function. What is the value associated to 0.975?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We know that for $X$ a standard Gaussian, we have\n",
    "$$\\mathrm{V@R}^\\alpha(X) = \\Phi^{-1}(\\alpha); \\qquad \\mathrm{ES}^\\alpha(X) = \\frac{1}{1-\\alpha}\\varphi(\\Phi^{-1}(\\alpha)).$$\n",
    "\n",
    "Therefore, we have \n",
    "$$\\phi(\\alpha) = \\Phi\\left(\\frac{1}{1-\\alpha} \\varphi(\\Phi^{-1}(\\alpha))\\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9903012596460189"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def phi_special(alpha):\n",
    "    \n",
    "    if alpha>=1 or alpha<=0:\n",
    "        raise ValueError('The variable alpha must be in between 0 and 1')\n",
    "    \n",
    "    return st.norm.cdf(st.norm.pdf(st.norm.ppf(alpha))/(1-alpha))\n",
    "    \n",
    "phi_special(0.975)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The above means that, if a distribution is standard Gaussian, we can create a connection between the value at risk at level 99% (approx) and Expected Shortfall at level 97.5%. As we will discuss later in the course, this has been used in the standard model under Basel 3 to define an easy backtest for expected shortfall"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "3. Assume that you have invested £100, equally, in two investments with P&L given respectively by a) A Gaussian random variable with mean 60 and sd 100; and b) An exponential random variable with mean 75. Assume further that both are independent. \n",
    "\n",
    "Calculate the value at risk and expected shortfall of your total P&L.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Since we are given directly the P&L of each investment, we do not really need to use the initial value: we simply sum up the P&L to find the total value. However, summing up these two distributions does not give a known distribution. Hence we will use the Monte Carlo approach to estimate the value at risk and expected shortfall at the given "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "sample_size = 1000000\n",
    "msample = rng.normal(60,100,sample_size) + rng.exponential(75,sample_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us illustrate the resulting distribution by looking at its pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram for total P&L')"
      ]
     },
     "execution_count": 36,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fzRBA/06G0PqHGZYi+WaS1411f2axTrXWTk7yoAxLYlySIdD8VpJjxra3GS/93oY86dbapRmCwrckWbjB39UZws5HttbeuSH19qC19u9Jfj7Jy3LzZSa+kuR/J7l/a+0ba9j+qUl+OcONB6/OELzePcldpq77cIYlPv4iyboMs4qvSvLpDOuvP2ZhbfSpcv+dYe3sv8sQwt4pN42/hWs2u/e3tfZnSX4uyRuTnJNhpvVtM/x9eWuSB7bWntla+3KGcPqGDGvBv2M968wDAHSpNs3NxAEAYOOoqk9lWG7h8B7DSAAAYGkCbAAAtlhVtU+SM5PcmGTX1tr5yxQBAAA6svXylwAAQL+q6n8m+YkMNyVc11q7oaq2T/LkJK8dL3uP8BoAADY/ZmADALBZq6o/TvKH48Mbklye5A656X4vX07yS+N6yAAAwGbEDGwAADZ3J2W4UeMjk+ySZOck30/ytQw3dnxra+3qTdc9AABgQ5mBDQAAAABAl7Za/hIAAAAAANj4BNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAl7be1B1gUFXfSnL7JOs2cVcAAAAAAFZj1yTfb63dY7UVCbD7cfttttlm5z333HPnTd0RAAAAAIANdfbZZ+fqq6+eS10C7H6s23PPPXf+whe+sKn7AQAAAACwwfbaa6988YtfXDePuqyBDQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRp603dAQBg87Driz+yqbvARrDulY/f1F0AAAD4ETOwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC7NLcCuql2q6u1VdWFVXVtV66rqdVW10wrr2Xkst26s58Kx3l3m0XZV3X4896nx+muq6uKq+lxVvaCqtltPO0+oqtOr6vKquqKqPltVz1jJ8wMAAAAAYDZzCbCrarckX0hyeJLPJXltkvOSHJXkM1V1xxnruWOSz4zlzh3r+dxY7xeq6p5zaHvnJP8zyQ1JPpLk+CTvTbLDQntVdftF2jkiyYeT/FySdyX5iyQ/leSdVfXqWZ4fAAAAAACz23pO9bw5yZ2THNlaO2HhYFUdn+ToJC9P8pwZ6nlFkt2THN9ae9FEPUcmef3YzkGrbPv8JDu21n443XhVvSvJr4/X/+nE8V2TvDrJpUke1FpbNx5/WZJ/TvKiqnp/a+0zMzxHAAAAAABmsOoZ2OMM6AOTrEvypqnTxyS5Msmh61uaY6xn+ySHjtcfO3X6jUm+neQxk7OwN6Tt1toNi4XXo/eO+3tPHf+tJLdN8saF8Hqs67IMoXsyW0APAAAAAMCM5rGEyP7j/pTW2o2TJ1prP0hyRpJtk+y9TD17J9kmyRljucl6bkxy8lR782x7wRPH/b9OHX/UuP/YImU+OnUNAAAAAABzMI8lRO4z7r+xxPlvZpglvXuSj6+ynoz1rLrtqto6yR+ND3dO8vAkD0hyWob1rWfqW2vtoqq6MskuVbVta+2qJfqy0O4Xlji1x/rKAQAAAADc0swjwN5x3F++xPmF43dYg3pW0/bWGZYZmXRikue21q7ZgL5tN1633gAbAAAAAIDZzOsmjpudMaSuqqokP5Xk0Un+JMnnq+qgybWu59zuXosdH2dmP3At2gQAAAAA2BzNYw3shVnJOy5xfuH499agnlW33Qb/2Vr7qyRPzrBcyBs3sG9LzdAGAAAAAGCF5hFgnzPud1/i/L3H/VLrVK+mnnm1nSRprZ2VIezeb9a+VdVdMywfcsFy618DAAAAADC7eQTYp437A6vqZvVV1Q5J9s2wLvRZy9RzVpKrk+w7lpusZ6sMN2OcbG+ebU+WuX2S66dOnTruD1qk2GOnrgEAAAAAYA5WHWC31s5NckqSXZM8b+r0cRlmJ5/YWrty4WBV7VFVe0zVc0WGmyhul+TYqXqOGOs/ubV23irbvl9V3W76eVTVbTIsHbJVko9MnX5HkmuTHFFVu06U2SnJS8aHb52uEwAAAACADTevmzg+N8mZSd5QVQckOTvJQ5Psn2H5jj+cuv7scV9Tx1+SYfmOF1bVA5J8LsmeSQ5OcnF+PKTekLafmeTwqjojybczLBnyUxlmeN8lw3IhvzNZoLX2rar63SRvyHCTx3cnuS7JU5PskuQ1rbXPLPrKAAAAAACwQeYSYLfWzq2qByV5WYZlNh6X5KIkr09yXGvtshnruaSq9klyTJJDkjw8ySUZZkC/tLV2wRzafm+S7ZPsM247JPl+kq8leU2SNy+2lnVr7YSqWpch3P7NDDO1v5bkj8YbQAIAAAAAMEfzmoGd1tr5SQ6f8drpmdeT5y5NctS4rUXbZyQ5Y9a6p8p+OMmHN6QsAAAAAAArM4+bOAIAAAAAwNwJsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOjS3ALsqtqlqt5eVRdW1bVVta6qXldVO62wnp3HcuvGei4c691lHm1X1d2q6vlV9dGJNi6pqn+sqicvUf9+VdXWs71yJc8RAAAAAIDlbT2PSqpqtyRnJrlzkg8l+XqShyQ5KslBVbVva+2SGeq541jP7klOTXJSkj2SHJ7k8VW1T2vtvFW2/fwkv5/kW0lOS/KdJHdP8uQkj66q17bWXrhEFz+R5PRFjn96uecGAAAAAMDKzCXATvLmDAHyka21ExYOVtXxSY5O8vIkz5mhnldkCK+Pb629aKKeI5O8fmznoFW2/bkk+7XWPjFZSVXtmeSsJEdX1V+31r6wSP9Ob60dO8PzAAAAAABglVa9hMg4A/rAJOuSvGnq9DFJrkxyaFVtt0w92yc5dLz+2KnTb0zy7SSPqap7rqbt1trfTYfX4/Gzk7x7fLjf+voKAAAAAMDam8ca2PuP+1NaazdOnmit/SDJGUm2TbL3MvXsnWSbJGeM5SbruTHJyVPtzbPtBT8c99cvcf5eVXVEVb2kqn6rqu49Y70AAAAAAKzQPJYQuc+4/8YS57+ZYZb07kk+vsp6MtYz77ZTVbdP8pQkLckpS1z26+M2We79SZ7dWrtsffVPXL/Y0iTJsNY3AAAAAACjeczA3nHcX77E+YXjd1iDeubSdlVVkrcl+ckkbxmXE5n03SQvTnK/JDskuVOSxyb5UobQ+8NVNY/XEgAAAACA0bxu4ri5e02SpyX5VJIXTp9srX01yVcnDl2R5GNVdWaSLyfZN8kTk3xouYZaa3stdnycmf3AlXYcAAAAAGBLNY9ZwwuznHdc4vzC8e+tQT2rbruq/jTJ0Uk+meRxrbVrl+nnj7TWvp/kb8aHj5i1HAAAAAAAy5vHDOxzxv3uS5xfuNHhUutUr6aeVbVdVa9N8oIkpyV5QmvtqmX6uJjvjvvtNqAsAAAAAABLmMcM7NPG/YHT60BX1Q4Zlte4KslZy9RzVpKrk+w7lpusZ6sMN2OcbG+D267BmzKE1/+Y5PEbGF4nyd7j/rwNLA8AAAAAwCJWHWC31s5NckqSXZM8b+r0cRlmJp/YWrty4WBV7VFVe0zVc0WSE8frj52q54ix/pNba+dNlNmQtivJnyd5bpKPJnlSa+3q9T3HqnrQEsd/I8mvJrkuyXvWVwcAAAAAACszr5s4PjfJmUneUFUHJDk7yUOT7J9h+Y4/nLr+7HFfU8dfkmS/JC+sqgck+VySPZMcnOTi/HhIvSFtvzTJszLM9v5ykhcPmfbNfLm19sGJx++rquuTfD7JBUlul+TBSR6S5Pokv91aW7dI3wAAAAAA2EBzCbBba+eOs5RfluSgJI9LclGS1yc5rrV22Yz1XFJV+yQ5JskhSR6e5JIk70jy0tbaBXNo+x7jfpskf7BEV/4qyQcnHr8lyaMzLEnyExmC9/9M8s4kr2ut/csszw8AAAAAgNnNawZ2WmvnJzl8xmt/bMrzxLlLkxw1bmvR9mFJDpu17rHMq5K8aiVlAAAAAABYnXncxBEAAAAAAOZOgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECXBNgAAAAAAHRJgA0AAAAAQJcE2AAAAAAAdEmADQAAAABAlwTYAAAAAAB0SYANAAAAAECX5hZgV9UuVfX2qrqwqq6tqnVV9bqq2mmF9ew8lls31nPhWO8u82i7qu5WVc+vqo9OtHFJVf1jVT15mb49oapOr6rLq+qKqvpsVT1jJc8PAAAAAIDZbD2PSqpqtyRnJrlzkg8l+XqShyQ5KslBVbVva+2SGeq541jP7klOTXJSkj2SHJ7k8VW1T2vtvFW2/fwkv5/kW0lOS/KdJHdP8uQkj66q17bWXrhI345IckKSS5K8K8l1SZ6a5J1Vdb/W2u8s+0IBAAAAADCzuQTYSd6cIUA+srV2wsLBqjo+ydFJXp7kOTPU84oM4fXxrbUXTdRzZJLXj+0ctMq2P5dkv9baJyYrqao9k5yV5Oiq+uvW2hcmzu2a5NVJLk3yoNbauvH4y5L8c5IXVdX7W2ufmeE5AgAAAAAwg1UvITLOgD4wybokb5o6fUySK5McWlXbLVPP9kkOHa8/dur0G5N8O8ljquqeq2m7tfZ30+H1ePzsJO8eH+43dfq3ktw2yRsXwuuxzGUZQvdktoAeAAAAAIAZzWMN7P3H/SmttRsnT7TWfpDkjCTbJtl7mXr2TrJNkjPGcpP13Jjk5Kn25tn2gh+O++unjj9q3H9skTIfnboGAAAAAIA5mEeAfZ9x/40lzn9z3O++BvXMq+1U1e2TPCVJS3LKrH1rrV2UYab3LlW17QztfGGxLcNa3wAAAAAAjOYRYO847i9f4vzC8TusQT1zabuqKsnbkvxkkreMy4lsSN92XOI8AAAAAAArNK+bOG7uXpPkaUk+leSFa9lQa22vxY6Ps7AfuJZtAwAAAABsTuYxA3u52ccLx7+3BvWsuu2q+tMkRyf5ZJLHtdauXUXflpqhDQAAAADACs0jwD5n3C+1zvS9x/1S61Svpp5VtV1Vr03yu0lOS/LY1toVK+1bVd01yXZJLmitXbVEeQAAAAAAVmgeAfZp4/7AqrpZfVW1Q5J9k1yV5Kxl6jkrydVJ9h3LTdazVZIDp9rb4LZr8KYkL0jyj0kev0z4fOq4P2iRc4+dugYAAAAAgDlYdYDdWjs3ySlJdk3yvKnTx2WYnXxia+3KhYNVtUdV7TFVzxVJThyvP3aqniPG+k9urZ23yrYryZ8neW6SjyZ5Umvt6mWe5juSXJvkiKradaKunZK8ZHz41mXqAAAAAABgBeZ1E8fnJjkzyRuq6oAkZyd5aJL9Myzf8YdT15897mvq+EuS7JfkhVX1gCSfS7JnkoOTXJwfD6k3pO2XJnlWhtneX07y4iHTvpkvt9Y+uPCgtfatqvrdJG9I8vmqeneS65I8NckuSV7TWvvMIn0DAAAAAGADzSXAbq2dW1UPSvKyDMtsPC7JRUlen+S41tplM9ZzSVXtk+SYJIckeXiSSzLMgH5pa+2CObR9j3G/TZI/WKIrf5Xkg1PtnFBV65L8TpLfzDB7/WtJ/qi19lezPD8AAAAAAGY3rxnYaa2dn+TwGa/9sSnPE+cuTXLUuK1F24clOWzWuqfKfjjJhzekLAAAAAAAKzOPmzgCAAAAAMDcCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC5tvak7AABAP3Z98Uc2dRfYCNa98vGbugsAADATM7ABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC4JsAEAAAAA6JIAGwAAAACALgmwAQAAAADokgAbAAAAAIAuCbABAAAAAOiSABsAAAAAgC7NLcCuql2q6u1VdWFVXVtV66rqdVW10wrr2Xkst26s58Kx3l3m1XZVPbOq/qyqPltVV1VVq6o/Xk/9+43XLLW9ciXPEQAAAACA5W09j0qqarckZya5c5IPJfl6kockOSrJQVW1b2vtkhnqueNYz+5JTk1yUpI9khye5PFVtU9r7bw5tP2aJDsmuSzJhUl2m/GpfiLJ6Ysc//SM5QEAAAAAmNFcAuwkb84QIB/ZWjth4WBVHZ/k6CQvT/KcGep5RYbw+vjW2osm6jkyyevHdg6aQ9tPT3J2a+3bVXVYknfM0LckOb21duyM1wIAAAAAsAqrXkJknAF9YJJ1Sd40dfqYJFcmObSqtlumnu2THDpef+zU6Tcm+XaSx1TVPVfbdmvtY621by/z1AAAAAAA2ITmsQb2/uP+lNbajZMnWms/SHJGkm2T7L1MPXsn2SbJGWO5yXpuTHLyVHvzbHtW96qqI6rqJVX1W1V17znVCwAAAADAlHksIXKfcf+NJc5/M8Ms6d2TfHyV9WSsZ95tz+rXx+1Hqur9SZ7dWrtslgqq6gtLnNpjlX0DAAAAANiizGMG9o7j/vIlzi8cv8Ma1DOvtpfz3SQvTnK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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {
      "image/png": {
       "height": 426,
       "width": 728
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.hist(msample, density=True)\n",
    "plt.title('Histogram for total P&L')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The P&L sample has mean 135.00 and standard deviation 124.85.\n"
     ]
    }
   ],
   "source": [
    "print('The P&L sample has mean {:.2f} and standard deviation {:.2f}.'.format(msample.mean(),msample.std() ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The pdf looks a bit schewed to the right. We therefore expect the losses to be less severe than a Gaussian with shared mean and variance. This is the effect of adding an exclusively postive variable with a fat(ish) tail like the exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(56.772695035703194, 101.16449784433254)"
      ]
     },
     "execution_count": 41,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_level = 0.95\n",
    "var_es_sample(msample,alpha_level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value at risk and ES at level  0.99  for the P&L are respectively:  (56.772695035703194, 101.16449784433254)\n"
     ]
    }
   ],
   "source": [
    "print('The value at risk and ES at level ',alpha,' for the P&L are respectively: ',var_es_sample(msample,alpha_level))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value at risk and ES at level  0.99  for a Gaussian with the same mean and sample are respectively:  70.35997532489128 122.52969401730198\n"
     ]
    }
   ],
   "source": [
    "print('The value at risk and ES at level ',alpha,' for a Gaussian with the same mean and sample are respectively: ', varisk(st.norm(135,124.85), alpha_level), es(st.norm(135,124.85), alpha_level))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
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