projet_optimisation_financiere.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partie 1\n",
    "Implémenter la méthode des treillis pour le calcul des prix d’options (pour les différents types d’options). \n",
    "On testera la méthode sur différentes instances en faisant varier les paramètres (N : le nombre de périodes, r : taux de crédit, d et u). \n",
    "On essayera de considérer aussi des instances assez larges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "import numpy as np\n",
    "import time\n",
    "import psutil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def assetTreeValue(n, S, u, d):  \n",
    "    asset = np.zeros((n+1,n+1))\n",
    "    asset[0,0] = S\n",
    "    for i in range(1,n+1):\n",
    "        asset[i,0] = asset[i-1,0]*u\n",
    "        for j in range(1,i+1):\n",
    "            asset[i,j] = asset[i-1,j-1]*d\n",
    "    return asset    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculationOptionPrice(n, assetValue, K, r, u, d, PutCall, optiontype):\n",
    "    value = np.zeros((n+1,n+1))\n",
    "    proba = (1+r-d)/(u-d)\n",
    "    \n",
    "    for j in range(n+1):\n",
    "        if PutCall==\"C\": # Call\n",
    "            payoff = max(0, (assetValue[n,j]-K))\n",
    "            value[n,j] = payoff\n",
    "        elif PutCall==\"P\": #Put\n",
    "            payoff = max(0, (K-assetValue[n,j]))\n",
    "            value[n,j] = payoff\n",
    "    \n",
    "    if optiontype == \"USA\":\n",
    "         for i in range(n-1,-1,-1):\n",
    "            for j in range(i+1):\n",
    "                if PutCall==\"P\":\n",
    "                    value[i,j] = max(0, K-assetValue[i,j], (1/1+r)*(proba*value[i+1,j]+(1-proba)*value[i+1,j+1]))\n",
    "                elif PutCall==\"C\":\n",
    "                    value[i,j] = max(0, assetValue[i,j]-K, (1/1+r)*(proba*value[i+1,j]+(1-proba)*value[i+1,j+1]))\n",
    "    \n",
    "    if optiontype == \"EUR\":\n",
    "         for i in range(n-1,-1,-1):\n",
    "            for j in range(i+1):\n",
    "                value[i,j] = (1/1+r)*(proba*value[i+1,j]+(1-proba)*value[i+1,j+1])\n",
    "                    \n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Option value :  2.360466633862231\n"
     ]
    }
   ],
   "source": [
    "asset = assetTreeValue(4, 100, 1.0425, 0.9592)\n",
    "optionvalue = calculationOptionPrice(4, asset, 98, 0.00077, 1.0425, 0.9592, \"P\", \"USA\")\n",
    "print('Option value : ', optionvalue[0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Temps d'exécution en fonction de N (nombre de période)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "execution_time_Eur = []\n",
    "execution_time_USD = []\n",
    "series = []\n",
    "\n",
    "    \n",
    "for i in range(3, n):\n",
    "    series.append(i)\n",
    "\n",
    "    # Calcul Option USA\n",
    "    tps_USD1 = time.time()\n",
    "    asset_USD = assetTreeValue(i, 100, 1.1, 0.9)\n",
    "    optionvalue_USD = calculationOptionPrice(i, asset_USD, 91, 0.05, 1.1, 0.9, \"C\", \"USA\")\n",
    "    tps_USD2 = time.time()\n",
    "    execution_time_USD.append((tps_USD2-tps_USD1)*1000)\n",
    "\n",
    "    # Calcul Option EUR\n",
    "\n",
    "    tps_EUR1 = time.time()\n",
    "    asset_EUR = assetTreeValue(i, 100, 1.1, 0.9)\n",
    "    optionvalue_EUR = calculationOptionPrice(i, asset_EUR, 91, 0.05, 1.1, 0.9, \"C\", \"EUR\")\n",
    "    tps_EUR2 = time.time()\n",
    "    execution_time_Eur.append((tps_EUR2-tps_EUR1)*1000)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 540x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7.5,5)) #Changer taille de la figure\n",
    "plt.plot(series, execution_time_USD, label='Option américaine') # Plot l'USD \n",
    "plt.plot(series, execution_time_Eur, label='Option européenne')  # Plot l'EUR\n",
    "\n",
    "\n",
    "plt.xlabel(\"N (périodes)\")\n",
    "plt.ylabel(\"Execution time (ms)\")\n",
    "plt.legend(framealpha=1, frameon=True);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### CPU en fonction de N (nombre de période)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[34.0, 28.2, 30.0, 38.2, 30.0, 40.8, 29.4]\n",
      "[32.2, 37.0, 27.5, 21.8, 35.7, 33.8, 35.3]\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "series = []\n",
    "CPU_USA = []\n",
    "CPU_EUR = []\n",
    "\n",
    "\n",
    "def CalculateCPU_USA(i):\n",
    "    asset_USD = assetTreeValue(i, 100, 1.1, 0.9)\n",
    "    optionvalue_USD = calculationOptionPrice(i, asset_USD, 91, 0.05, 1.1, 0.9, \"C\", \"USA\")\n",
    "    CPU_USA.append(psutil.cpu_percent())\n",
    "    \n",
    "def CalculateCPU_EUR(i):\n",
    "    asset_EUR = assetTreeValue(i, 100, 1.1, 0.9)\n",
    "    optionvalue_EUR = calculationOptionPrice(i, asset_EUR, 91, 0.05, 1.1, 0.9, \"C\", \"EUR\")\n",
    "    CPU_EUR.append(psutil.cpu_percent())\n",
    "    \n",
    "for i in range(3,n):\n",
    "    series.append(i)\n",
    "    time.sleep(2)\n",
    "    CalculateCPU_USA(i)\n",
    "    time.sleep(2)\n",
    "    CalculateCPU_EUR(i)\n",
    "\n",
    "print(CPU_USA)\n",
    "print(CPU_EUR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7.5,5)) #Changer taille de la figure\n",
    "plt.plot(series, CPU_USA, label='Option américaine') # Plot l'USD \n",
    "plt.plot(series, CPU_EUR, label='Option européenne') # Plot l'USD \n",
    "\n",
    "\n",
    "plt.xlabel(\"N (périodes)\")\n",
    "plt.ylabel(\"CPU utilization as a percentage\")\n",
    "plt.legend(framealpha=1, frameon=True);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prix option Put en fonction des périodes N (nombre de période)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "price_Put_Eur = []\n",
    "price_Put_USD = []\n",
    "series = []\n",
    "\n",
    "for i in range(3, n):\n",
    "    series.append(i)\n",
    "    asset = assetTreeValue(i, 100, 1.1, 0.9)\n",
    "        \n",
    "    # Put\n",
    "    optionvalue_Put_USD = calculationOptionPrice(i, asset, 98, 0.05, 1.1, 0.9, \"P\", \"USA\")\n",
    "    price_Put_USD.append(optionvalue_Put_USD[0][0])\n",
    "\n",
    "    # Put\n",
    "    optionvalue_Put_Eur = calculationOptionPrice(i, asset, 98, 0.05, 1.1, 0.9, \"P\", \"EUR\")\n",
    "    price_Put_Eur.append(optionvalue_Put_Eur[0][0])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7.5,5))  #Changer taille de la figure\n",
    "\n",
    "plt.plot(series, price_Put_USD, label='Put américain')  # Plot l'EUR\n",
    "\n",
    "plt.plot(series, price_Put_Eur, label='Put européen')  # Plot l'USD \n",
    "\n",
    "plt.xlabel(\"N (périodes)\")\n",
    "plt.ylabel(\"Price(euro)\")\n",
    "plt.legend(framealpha=1, frameon=True);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prix option Call en fonction des périodes N (nombre de période)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100\n",
    "price_Call_USD = []\n",
    "price_Call_Eur = []\n",
    "series = []\n",
    "\n",
    "for i in range(3, n):\n",
    "    series.append(i)\n",
    "    asset = assetTreeValue(i, 100, 1.04, 0.96)\n",
    "    \n",
    "    # Call\n",
    "    optionvalue_Call_USD = calculationOptionPrice(i, asset, 98, 0.04, 1.04, 0.96, \"C\", \"USA\")\n",
    "    price_Call_USD.append(optionvalue_Call_USD[0][0])\n",
    "    #print(optionvalue_Call_USD)\n",
    "    \n",
    "     # Call\n",
    "    optionvalue_Call_Eur = calculationOptionPrice(i, asset, 98, 0.04, 1.04, 0.96, \"C\", \"EUR\")\n",
    "    price_Call_Eur.append(optionvalue_Call_Eur[0][0])\n",
    "    #print(optionvalue_Call_Eur)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7.5,5))  #Changer taille de la figure\n",
    "\n",
    "plt.plot(series, price_Call_USD, label='Call américain')\n",
    "plt.plot(series, price_Call_Eur, label='Call européenn')  # Plot l'USD \n",
    "\n",
    "plt.xlabel(\"N (périodes)\")\n",
    "plt.ylabel(\"Price(euro)\")\n",
    "plt.legend(framealpha=1, frameon=True);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prix option de 5 périodes, 100 euros au départ, en fonction de K (strike) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "price_Put_Eur = []\n",
    "price_Put_USD = []\n",
    "\n",
    "price_Call_USD = []\n",
    "price_Call_Eur = []\n",
    "series = []\n",
    "\n",
    "\n",
    "for i in range(75,125):\n",
    "    series.append(i)\n",
    "    asset = assetTreeValue(10, 100, 1.1, 0.9)\n",
    "        \n",
    "    # Put USA\n",
    "    optionvalue_Put_USD = calculationOptionPrice(5, asset, i, 0.05, 1.1, 0.9, \"P\", \"USA\")\n",
    "    price_Put_USD.append(optionvalue_Put_USD[0][0])\n",
    "\n",
    "    # Put EUR\n",
    "    optionvalue_Put_Eur = calculationOptionPrice(5, asset, i, 0.05, 1.1, 0.9, \"P\", \"EUR\")\n",
    "    price_Put_Eur.append(optionvalue_Put_Eur[0][0])\n",
    "    \n",
    "    # Call USA\n",
    "    optionvalue_Call_USD = calculationOptionPrice(5, asset, i, 0.05, 1.1, 0.9, \"C\", \"USA\")\n",
    "    price_Call_USD.append(optionvalue_Call_USD[0][0])\n",
    "    \n",
    "    # Call EUR\n",
    "    optionvalue_Call_Eur = calculationOptionPrice(5, asset, i, 0.05, 1.1, 0.9, \"C\", \"EUR\")\n",
    "    price_Call_Eur.append(optionvalue_Call_Eur[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7.5,5))  #Changer taille de la figure\n",
    "\n",
    "plt.plot(series, price_Put_USD, label='Put américain')  # Plot l'EUR\n",
    "\n",
    "plt.plot(series, price_Put_Eur, label='Put européen')  # Plot l'USD \n",
    "\n",
    "plt.plot(series, price_Call_USD, label='Call américain')\n",
    "\n",
    "plt.plot(series, price_Call_Eur, label='Call européenn')\n",
    "\n",
    "plt.xlabel(\"Strike price (euros)\")\n",
    "plt.ylabel(\"Price (euros)\")\n",
    "plt.legend(framealpha=1, frameon=True);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partie 2\n",
    "\n",
    "Ecrire le modèle qui permet de minimiser la CVaR pour une probabilité donnée  (On donne le modèle général avec un nombre d’actifs n, un nombre de scénarios S, un vecteur rendement  et un rendement minimum R."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics\\Partie 2.png\" width=\"480\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# X[0] Gamma, X[1...N] Actifs risqués \n",
    "def func_minimise_ES(X):\n",
    "    loose_function = 0\n",
    "    for i in range(S):\n",
    "        for j in range (1, X.size):   \n",
    "            loose_function = loose_function + max(((b[j]-Y[i][j-1])*X[j]-X[0]),0)\n",
    "    return X[0] + (1/(1-alpha)*S)*loose_function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S fois cette contrainte\n",
    "def constraint1(X,s):\n",
    "    sum = 0\n",
    "    for j in range (1,X.size):\n",
    "        sum = sum + (b[j]-Y[s][j-1])*X[j]\n",
    "    return max((sum-X[0]),0) - (sum-X[0])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S fois cette contrainte\n",
    "def constraint2(X,s):\n",
    "    sum = 0\n",
    "    for j in range (1,X.size):\n",
    "        sum = sum + (b[j]-Y[s][j-1])*X[j]\n",
    "    \n",
    "    return max((sum-X[0]),0)-0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constraint3(X):\n",
    "    sum = 1\n",
    "    for i in range(1,X.size):\n",
    "        sum = sum - X[i]\n",
    "    \n",
    "    return sum\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def minimise_ES_constraint4(X):\n",
    "    sum = 0\n",
    "    for i in range(1,X.size):\n",
    "        sum += X[i]*E[i]\n",
    "        \n",
    "    return sum - R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pour que la somme des X soit toujours un reel \n",
    "def constraint5(X):\n",
    "    return np.sum(np.iscomplex(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fonctions pour la compréhension logique : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculatePortfolioRendement(X):\n",
    "    sum = 0\n",
    "    for i in range(1,X.size):\n",
    "        sum += X[i]*E[i]\n",
    "    return sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loose_function(X):\n",
    "    loose_function = 0\n",
    "    for i in range(S):\n",
    "        for j in range (1, X.size):\n",
    "            loose_function = loose_function + max(((b[j]-Y[i][j-1])*X[j]-X[0]),0)\n",
    "    return loose_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Générateur de scénarios :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random as rd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generateY(X,S):\n",
    "    Y = []\n",
    "    for i in range(S):\n",
    "        Z = []\n",
    "        for j in range(1,X.size):\n",
    "            Z.append(X[j] + rd.randint(0, 10)) \n",
    "        Y.append(Z)\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculer VaR initial (Test) :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Méthode de Calcul de la Variance : https://blog.quantinsti.com/calculating-covariance-matrix-portfolio-variance/ <br>\n",
    "Expected portfolio variance = WT * (Covariance Matrix) * W\n",
    "<br>\n",
    "La matrice de covariance est donnée, par besoin de valeurs historiques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculatePortfolioVariance(X):\n",
    "    assets = X\n",
    "    assets = np.delete(assets, 0)\n",
    "    variance = (assets)*Cov*(assets.reshape((-1, 1)))\n",
    "    return variance "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La volatilité du portefeuille est la racine carré de la variance :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculatePortfolioVolatity(X):\n",
    "    variance = calculatePortfolioVariance(X)\n",
    "    variance = variance[0][0]\n",
    "    return mt.pow(variance, (0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Méthode de calcul de la VaR paramétrique : https://meritis.fr/vous-saurez-tout-sur-la-var/ <br>\n",
    "VaR = z*sigma - R <br>\n",
    "    - R : rentabilité du portefeuille\n",
    "    - z : interval de confiance de la loi normal obtenue grâce à norm\n",
    "    - sigma : volatility du portefeuille"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculatePortfolioVaR(X, alpha):\n",
    "    rend = calculatePortfolioRendement(X)\n",
    "    z = norm.ppf(1-alpha)\n",
    "    sigma = calculatePortfolioVolatity(X)\n",
    "    VaR_n = abs(z*sigma - rend)\n",
    "    return  round(VaR_n*100,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exécution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math as mt\n",
    "from scipy.stats import norm\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### General Informations : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.999# Probabilité\n",
    "R = 0.001 # Rentabilité"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Assets Informations :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Réparition des actifs (X[0] => Gamma) X:  [1.    0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125] \n",
      "\n",
      "Prix des obligations b :  [  0.     9.73 128.8    3.93 126.8  132.19  29.7  166.14  25.9 ] \n",
      "\n",
      "Espérance de rendement E :  [0.         0.00116789 0.00019611 0.00044436 0.00019611 0.00078812\n",
      " 0.0002209  0.00021948 0.00026063] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "Nb_Assets = 8\n",
    "Valo = 10000 # fixe Valorisation fictive pour calculer la VaR fictive \n",
    "\n",
    "X = np.array([1, 0.125,0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]) # Réparitition des actifs,  Attention : X[0] == gamma\n",
    "b = np.array([0, 9.73, 128.80, 3.93, 126.80, 132.19, 29.70, 166.14, 25.90]) # Prix des obligations, b[0]=0 pour la fonction objective\n",
    "E = np.array([0, 0.001167892, 0.00019611, 0.000444357, 0.00019611,0.000788123, 0.000220896, 0.00021948, 0.000260628]) # Espérence de rendement des actifs\n",
    "\n",
    "#Cov = np.matrix([[0.02778, 0.00387, 0.00021], [0.00387, 0.01112, -0.00020], [0.00021, -0.00020, 0.00115] ])\n",
    "\n",
    "\n",
    "print('Réparition des actifs (X[0] => Gamma) X: ', X, '\\n')\n",
    "print('Prix des obligations b : ', b, '\\n')\n",
    "print('Espérance de rendement E : ', E, '\\n')\n",
    "#print('Covarinace des actifs Cov :', Cov, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scénarios Informations :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "S = 10 # Nombre de scénarios\n",
    "Y = np.array(generateY(X,S)) # vecteur de probabilités\n",
    "#print('Vecteur de probabilité Y : ', Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lancement :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Function initale :  6623500.999999994\n",
      "Function de perte initial :  662.35\n",
      "Gamma initial :  1.0\n",
      "1 - Répartition initiale :  0.0\n",
      "Rendement initial :  0.00043669950000000004\n",
      "Rendement initial - Rendement espéré :  -0.0005633005 \n",
      "\n",
      "`xtol` termination condition is satisfied.\n",
      "Number of iterations: 496, function evaluations: 4960, CG iterations: 1512, optimality: 1.78e+00, constraint violation: 1.53e-08, execution time: 1.1e+01 s.\n",
      " barrier_parameter: 2.048000000000001e-09\n",
      " barrier_tolerance: 2.048000000000001e-09\n",
      "          cg_niter: 1512\n",
      "      cg_stop_cond: 2\n",
      "            constr: [array([0.]), array([0.]), array([0.]), array([0.]), array([0.]), array([0.]), array([0.]), array([0.]), array([0.]), array([0.]), array([1.56829539]), array([0.62611669]), array([0.54503813]), array([3.30217885]), array([2.23745704]), array([1.83362675]), array([2.4457406]), array([3.32149709]), array([4.12839681]), array([0.93579857]), array([-1.52983349e-08]), array([1.72944914e-07]), array([6.05913039e+00, 7.82201726e-01, 2.14069376e-04, 1.76084996e-01,\n",
      "       3.96036344e-02, 2.66615320e-04, 9.22184041e-04, 1.33301050e-04,\n",
      "       5.73489875e-04])]\n",
      "       constr_nfev: [4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 4960, 0]\n",
      "       constr_nhev: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "       constr_njev: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "    constr_penalty: 1.0\n",
      "  constr_violation: 1.529833493891207e-08\n",
      "    execution_time: 11.43922209739685\n",
      "               fun: 6.059130390034437\n",
      "              grad: array([1., 0., 0., 0., 0., 0., 0., 0., 0.])\n",
      "               jac: [array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[ -1.        ,   3.60499996, 124.67500001,  -1.19499999,\n",
      "        123.67500001, 129.065     ,  29.57499999, 161.01500005,\n",
      "         17.77499998]]), array([[ -1.        ,   3.60499996, 124.67500001,  -5.19499999,\n",
      "        117.67499995, 129.065     ,  27.57499999, 156.01499999,\n",
      "         21.77499998]]), array([[ -1.        ,   1.60500002, 128.67500001,   2.80500001,\n",
      "        119.67500001, 128.065     ,  25.57500005, 157.01499999,\n",
      "         15.77499998]]), array([[ -1.        ,   5.60500002, 119.67500007,  -0.19499993,\n",
      "        123.67500007, 128.06500006,  22.57500005, 157.01499999,\n",
      "         20.7750001 ]]), array([[ -1.        ,   3.60500002, 124.67500007,   2.80499995,\n",
      "        122.67499995, 132.06499994,  28.57500005, 165.01499999,\n",
      "         24.77499998]]), array([[ -1.        ,   4.60500002, 118.67500001,  -3.19499999,\n",
      "        119.67500001, 129.065     ,  22.57499999, 159.01499999,\n",
      "         20.77499998]]), array([[ -1.        ,   3.6049999 , 120.67499995,   3.80499995,\n",
      "        123.67500007, 123.06500006,  27.57500005, 158.01499999,\n",
      "         20.7750001 ]]), array([[ -1.        ,   5.60500002, 121.67499995,   0.80500007,\n",
      "        119.67499995, 126.06500006,  25.57500005, 158.01499999,\n",
      "         18.77499998]]), array([[ -1.        ,   7.60500002, 120.67499995,  -4.19500017,\n",
      "        122.67499995, 130.06499994,  27.57500005, 160.01499999,\n",
      "         20.7750001 ]]), array([[ -1.        ,   3.60500002, 121.67500007,  -5.19499993,\n",
      "        125.67500007, 128.065     ,  22.57499999, 161.01500005,\n",
      "         17.77499998]]), array([[ 0., -1., -1., -1., -1., -1., -1., -1., -1.]]), array([[0.        , 0.00116789, 0.00019611, 0.00044436, 0.00019611,\n",
      "        0.00078812, 0.0002209 , 0.00021948, 0.00026063]]), array([[1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "       [0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
      "       [0., 0., 1., 0., 0., 0., 0., 0., 0.],\n",
      "       [0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
      "       [0., 0., 0., 0., 1., 0., 0., 0., 0.],\n",
      "       [0., 0., 0., 0., 0., 1., 0., 0., 0.],\n",
      "       [0., 0., 0., 0., 0., 0., 1., 0., 0.],\n",
      "       [0., 0., 0., 0., 0., 0., 0., 1., 0.],\n",
      "       [0., 0., 0., 0., 0., 0., 0., 0., 1.]])]\n",
      "   lagrangian_grad: array([ 0.9553646 ,  0.79617143,  1.05954557,  1.21514187,  0.80494779,\n",
      "        1.29696166,  0.09337252,  1.77508304, -0.04260551])\n",
      "           message: '`xtol` termination condition is satisfied.'\n",
      "            method: 'tr_interior_point'\n",
      "              nfev: 4960\n",
      "              nhev: 0\n",
      "               nit: 496\n",
      "             niter: 496\n",
      "              njev: 496\n",
      "        optimality: 1.7750830409348284\n",
      "            status: 2\n",
      "           success: True\n",
      "         tr_radius: 1.0000000000000005e-09\n",
      "                 v: [array([-1.48184488e+13]), array([-2.82806312e+11]), array([1.04691348e+12]), array([-5.20901679e+11]), array([-2.04730457e+11]), array([3.27323835e+11]), array([6.28246889e+10]), array([6.27991161e+10]), array([-1.86208606e+11]), array([-3.09860182e+10]), array([-0.00550409]), array([-0.03222993]), array([0.14692955]), array([-0.00134422]), array([0.00483121]), array([-0.00611803]), array([0.00270003]), array([0.00236234]), array([-0.00144798]), array([-0.06554348]), array([0.66872113]), array([1421.26042958]), array([ 0.        , -0.05216399, -4.93105834,  0.27405801, -3.81155205,\n",
      "       -4.82503028, -0.84294625, -4.65173378, -0.13247036])]\n",
      "                 x: array([6.05913039e+00, 7.82201726e-01, 2.14069376e-04, 1.76084996e-01,\n",
      "       3.96036344e-02, 2.66615320e-04, 9.22184041e-04, 1.33301050e-04,\n",
      "       5.73489875e-04]) \n",
      "\n",
      "Function finale :  6.059130390034437\n",
      "Function de perte finale :  0\n",
      "Gamma final :  6.059130390034437\n",
      "1 - Répartition obtenue :  -1.529833493891207e-08\n",
      "Rendement final :  0.0010001729449136724\n",
      "Rendement final - Rendement espéré :   1.7294491367236993e-07 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Function initale : ', func_minimise_ES(X))\n",
    "#print('VaR initial VaR : ', calculatePortfolioVaR(X, alpha))\n",
    "print('Function de perte initial : ', loose_function(X))\n",
    "print('Gamma initial : ', X[0])\n",
    "print('1 - Répartition initiale : ', constraint3(X))\n",
    "print('Rendement initial : ', calculatePortfolioRendement(X))\n",
    "print('Rendement initial - Rendement espéré : ', minimise_ES_constraint4(X), '\\n')\n",
    "\n",
    "\n",
    "# constraints\n",
    "Const1 = [] # S*contrainte \n",
    "Const2 = [] # S*contrainte\n",
    "for i in range(S):\n",
    "    Const1.append({'type':'ineq','args' : (i,) , 'fun': constraint1})\n",
    "    Const2.append({'type':'ineq','args' : (i,)  , 'fun': constraint2}) \n",
    "\n",
    "ineq_cons = []\n",
    "ineq_cons = (Const1 + Const2 + [{'type':'eq','fun': constraint3}, {'type':'ineq','fun': minimise_ES_constraint4}])\n",
    "\n",
    "\n",
    "# bonds xxx\n",
    "bond = (0, 1.0)\n",
    "ineq_bond = ((None, None),)\n",
    "for i in range(Nb_Assets):\n",
    "    ineq_bond = ineq_bond + (bond,) # x1 >= 0, x2 >= 0, ...\n",
    "\n",
    "\n",
    "\n",
    "sol = minimize(func_minimise_ES,\n",
    "                   x0=X, \n",
    "                   method='trust-constr',  # quand S petit, utiliser 'SLSQP' \n",
    "                   bounds=ineq_bond, \n",
    "                   options={'disp': True},\n",
    "                   constraints=ineq_cons)\n",
    "print(sol, '\\n')\n",
    "Res = sol.x\n",
    "\n",
    "print('Function finale : ', func_minimise_ES(Res))\n",
    "#print('VaR final VaR : ', calculatePortfolioVaR(Res, alpha))\n",
    "print('Function de perte finale : ', loose_function(Res))\n",
    "print('Gamma final : ', Res[0])\n",
    "print('1 - Répartition obtenue : ', constraint3(Res))\n",
    "print('Rendement final : ', calculatePortfolioRendement(Res))\n",
    "print('Rendement final - Rendement espéré :  ', minimise_ES_constraint4(Res), '\\n')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partie 3\n",
    "\n",
    "Considérons le modèle de Markowitz maximisant le rendement du portefeuille et assurant une CVaR  ne dépassant pas un certain seuil.  \n",
    "Ecrire le modèle correspondant et le résoudre pour certaines données aléatoires. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"pics\\Partie 3.png\" width=\"494\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import linprog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Définition des nouvelles varibales \n",
    "\n",
    "J = np.array([0, 0.50, 0.25, 0.25]) # Ensemble d'indices sur les différentes valeurs disponibles\n",
    "U = np.array([0, 1, 3, 4 ]) # Risque maximal toléré pour une valeur Alpha j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# X[0] Gamma, X[1...N] Actifs risqués \n",
    "def func_maximise_yield(X):\n",
    "    rendement = 0\n",
    "    for i in range(1,X.size):\n",
    "        rendement += X[i]*E[i]\n",
    "    return rendement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S fois cette contrainte\n",
    "def maximise_yield_constraint1(X,alpha_j):\n",
    "    sum = 0\n",
    "    for i in range(S):\n",
    "        loose_function = 0\n",
    "        for j in range (1, X.size):\n",
    "            loose_function = loose_function + max(((b[j]-Y[i])*X[j]-X[0]),0)\n",
    "            \n",
    "    return U[alpha_j] - (X[0] + (1/(1-alpha)*S)*loose_function) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration limit reached    (Exit mode 9)\n",
      "            Current function value: 0.0042663511016504865\n",
      "            Iterations: 100\n",
      "            Function evaluations: 1280\n",
      "            Gradient evaluations: 99\n",
      "     fun: 0.0042663511016504865\n",
      "     jac: array([0.     , 0.1073 , 0.00415, 0.0627 , 0.1045 , 0.1235 ])\n",
      " message: 'Iteration limit reached'\n",
      "    nfev: 1280\n",
      "     nit: 100\n",
      "    njev: 99\n",
      "  status: 9\n",
      " success: False\n",
      "       x: array([9.98525120e+00, 2.50350475e-06, 9.98014869e-01, 1.98275174e-03,\n",
      "       1.66979327e-08, 3.96356454e-09]) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# constraints\n",
    "Max_Const1 = [] # S*contrainte \n",
    "Max_Const2 = [] # S*contrainte \n",
    "Max_Const3 = [] # S*contrainte\n",
    "\n",
    "for i in range(1, J.size):\n",
    "    Max_Const1.append({'type':'ineq','args' : (i,) , 'fun': maximise_yield_constraint1})\n",
    "        \n",
    "for i in range(S):\n",
    "    Max_Const2.append({'type':'ineq','args' : (i,)  , 'fun': constraint2})\n",
    "    Max_Const3.append({'type':'ineq','args' : (i,)  , 'fun': constraint2})\n",
    "\n",
    "Max_ineq_cons = []\n",
    "Max_ineq_cons = (Max_Const1 + Max_Const2 + Max_Const3 +[{'type':'eq','fun': constraint3}])\n",
    "             \n",
    "\n",
    "\n",
    "# bonds \n",
    "bond = (0, 1.0)\n",
    "Max_ineq_bond = ((None, None),)\n",
    "for i in range(Nb_Assets):\n",
    "    Max_ineq_bond = Max_ineq_bond + (bond,) # x1 >= 0, x2 >= 0, ...\n",
    "\n",
    "\n",
    "sol = minimize(func_maximise_yield,\n",
    "               x0=X, \n",
    "               method='SLSQP',  # Il faut trouver la bonne méthode\n",
    "               bounds=Max_ineq_bond, \n",
    "               options={'disp': True},\n",
    "               constraints=Max_ineq_cons)\n",
    "print(sol, '\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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