{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6f883584-ca8b-4193-82bd-eca78426165e",
   "metadata": {},
   "source": [
    "# Méthode de Monte Carlo\n",
    "\n",
    "Tout d'abord, on illustre numériquement les deux résultats probabilistes sur lesquels reposent la méthode dite de Monte Carlo: \n",
    "\n",
    "- la loi forte de grands nombres,\n",
    "- le théorème central limit (TCL).\n",
    "\n",
    "On considère ensuite un premier exemple d'estimateur de Monte Carlo et l'importance de l'intervalle de confiance (IC) dans lequel se trouve la valeur recherchée avec probabilité grande (0.95). \n",
    "\n",
    "Enfin on applique la méthode de Monte Carlo à un exemple multidimensionnel où on illustre l'efficacité de 2 méthodes de réduction de variance: \n",
    "\n",
    "- variables antithétiques, \n",
    "- variable de contrôle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2e046f21-4713-4bfc-b2d0-32073d10d250",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_theme() \n",
    "from numpy.random import default_rng\n",
    "rng = default_rng()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc0d798f-524f-46de-aa81-2e7107a546d5",
   "metadata": {},
   "source": [
    "## Illustration de la loi des grands nombres\n",
    "\n",
    "Soit $(X_n)_{n \\ge 1}$ une suite de variables aléatoires _i.i.d._ de carré intégrable. On définit les suites $(m_n)_{n \\ge 1}$ et $(\\sigma_n^2)_{n \\ge 2}$ (non définie pour $n = 1$) de la façon suivante\n",
    "\n",
    "$$\n",
    "  m_n = \\frac{1}{n} \\sum_{k=1}^n X_k \\qquad \\text{et} \\qquad \n",
    "  \\sigma_n^2 = \\frac{1}{n-1} \\sum_{k=1}^n (X_k - m_n)^2 \\quad \\text{pour} \\; n \\ge 2\n",
    "$$\n",
    "et on veut illustrer la Loi Forte des Grands Nombres et le Théorème Central Limite (étendu en utilisant le lemme de Slutsky pour remplacer $\\sigma^2 = \\mathrm{var}(X_1)$ par l'estimateur $\\sigma_n^2$) c'est à dire les convergences\n",
    "\n",
    "$$\n",
    "  m_n \\xrightarrow{p.s.} m \\qquad \\text{et} \\qquad \n",
    "  \\sqrt{n} \\Bigl(\\frac{m_n - m}{\\sigma_n}\\Bigr) \\xrightarrow{\\mathcal{L}} \\mathcal{N}(0, 1).\n",
    "$$\n",
    "\n",
    "Plus précisément on construit l'intervalle de confiance (asymptotique) à 95% à partir du TCL c'est à dire\n",
    "\n",
    "$$\n",
    "  \\text{pour $n$ grand} \\quad \\mathbf{P} \\biggl( m \\in \n",
    "  \\biggl[\n",
    "    m_n - \\frac{1.96 \\sigma_n}{\\sqrt{n}}, \n",
    "    m_n + \\frac{1.96 \\sigma_n}{\\sqrt{n}}\n",
    "  \\biggr] \\biggr) \\simeq 0.95\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "853c2b0a-e6d8-40f1-a3af-f1732ef4ea2d",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: LFGN loi uniforme\n",
    "\n",
    "Reproduire le tracé suivant où les points (les croix 'x') sont les réalisations $X_n$ (en fonction de $n$) de loi uniforme sur $[-4,8]$. La ligne bleue (couleur 'C0', première couleur de la palette utilisée) correspond à la moyenne $m$, la courbe orangée (couleur 'C1') correspond à la suite $m_n$ et les lignes grises correspondent aux bornes de l'intervalle de confiance. La zone de confiance en jaune s'obtient par la méthode `fill_between` de `ax`.\n",
    "\n",
    "![](img/tcl_unif.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d1738bc2-91f6-42fb-9b1b-c525cbbf9109",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 300\n",
    "sample = rng.uniform(size = N, low = -4, high = 8)\n",
    "\n",
    "n = np.arange(1, N+1)\n",
    "mn = np.cumsum(sample) / n\n",
    "sum_squares = np.cumsum(sample**2)\n",
    "# attention: les vecteurs vn, ic, upper et lower sont définis pour n >= 2\n",
    "vn = (sum_squares - n*mn**2)[1:] / (n[1:]-1)  # on développe le carré\n",
    "ci_size = 1.96*np.sqrt(vn / n[1:])\n",
    "upper = mn[1:] + ci_size\n",
    "lower = mn[1:] - ci_size\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(n, sample, marker=\"x\", color='lightgrey')\n",
    "ax.axhline(y=2, color='C0', label=\"Valeur exacte\")\n",
    "ax.plot(n, mn, color='C1', label=\"Valeur de l'estimateur\")\n",
    "ax.fill_between(n[1:], lower, upper, facecolor='lightyellow', \n",
    "                edgecolor='grey', label=\"Zone de confiance à 95%\")\n",
    "ax.set(xlabel = \"Itération $n$\", \n",
    "       ylabel = \"Valeur de l'estimateur et des bornes de confiance\")\n",
    "ax.legend(loc='upper right')\n",
    "ax.set_ylim(-4, 8)\n",
    "#plt.savefig('img/tcl_unif.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c165f34-971d-43d3-92c9-5bc41ef1a5e6",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: LFGN loi de Cauchy\n",
    "\n",
    "Reprendre rapidement l'exemple précédent en remplaçant la loi uniforme par la loi de Cauchy. On obtient des réalisations de la loi de Cauchy en utilisant la méthode `standard_cauchy` de l'objet `rng`. Répliquer plusieurs fois le tracé (avec l'axe des ordonnées restreint à $[-10,10]$) pour différentes valeurs de $n=100\\,000$. Qu'en pensez-vous? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "56181a98-0d27-4033-971a-4c226efd1940",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100000\n",
    "sample = rng.standard_cauchy(size = N)\n",
    "\n",
    "n = np.arange(1, N+1)\n",
    "mn = np.cumsum(sample) / n\n",
    "sum_squares = np.cumsum(sample**2)\n",
    "# attention: les vecteurs vn, ic, upper et lower sont définis pour n >= 2\n",
    "vn = (sum_squares - n*mn**2)[1:] / (n[1:]-1)\n",
    "ci_size = 1.96*np.sqrt(vn / n[1:])\n",
    "upper = mn[1:] + ci_size\n",
    "lower = mn[1:] - ci_size\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(n, sample, marker=\"x\", color='lightgrey')\n",
    "ax.axhline(y=0, color='C0', label=\"Valeur exacte\")\n",
    "ax.plot(n, mn, color='C1', label=\"Valeur de l'estimateur\")\n",
    "ax.fill_between(n[1:], lower, upper, facecolor='lightyellow', \n",
    "                edgecolor='grey', label=\"Zone de confiance à 95%\")\n",
    "ax.set(xlabel = \"Itération $n$\", \n",
    "       ylabel = \"Valeur de l'estimateur et des bornes de confiance\")\n",
    "ax.legend(loc='upper right')\n",
    "ax.set_ylim((-10,10))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68ecfdc4-7625-41e1-8bcb-9a2e178ba238",
   "metadata": {},
   "source": [
    "## Illustration du TCL \n",
    "\n",
    "On veut illustrer la répartition de l'erreur renormalisée $\\displaystyle \\varepsilon_n = \\sqrt{n} \\Bigl(\\frac{m_n - m}{\\sigma_n}\\Bigr)$ pour différentes valeurs de $n$. Lorsque $n$ est grand cette erreur renormalisée est proche de la loi normale cenrée réduite, c'est ce qu'on veut vérifier numériquement. \n",
    "Pour illustrer cette répartition, il est nécessaire de répliquer un grand nombre de fois l'erreur c'est à dire de considérer un échantillon $(\\varepsilon_n^{(j)})_{j=1,\\dots,M}$ de taille $M$ et de constuire l'histogramme de cet échantillon.\n",
    "\n",
    "**Attention:** en pratique il n'est pas nécessaire de répliquer $M$ fois l'estimateur $m_n$ pour approcher $m$. L'estimateur de la variance $v_n$ suffit pour donner la zone de confiance autour de $m_n$. C'est une information importante donnée par le TCL."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31f6167f-b1a7-48a5-a766-21e39afbd9a0",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: TCL loi uniforme \n",
    "\n",
    "Dans le cas de la loi uniforme sur $[-4, 8]$ vérifier la répartition de l'erreur renormalisée $\\varepsilon_n$ pour $n = 10$ puis $n = 1\\,000$ à partir d'un échantillon de taille $M = 100\\,000$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3d5082d2-3a15-4cba-b9d6-a7d9c5f3f12b",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_error(ax, n, M = 100000):\n",
    "    sample = rng.uniform(size = (M, n), low = -4, high = 8)\n",
    "\n",
    "    means = np.mean(sample, axis = 1) \n",
    "    sigms = np.std(sample, axis = 1, ddof=1)\n",
    "    errs = np.sqrt(n) * (means - 2) / sigms \n",
    "\n",
    "    ax.hist(errs, bins=50, density=True, label=\"distribution empirique\")\n",
    "    xx = np.linspace(-5, 5, 10000)\n",
    "    ax.plot(xx, stats.norm.pdf(xx), label=\"densité gaussienne\")\n",
    "    ax.set(title = f\"n = {n}\")\n",
    "    ax.legend()\n",
    "    return ax\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, sharey=True, \n",
    "                               figsize=(10,6), layout='tight')\n",
    "fig.suptitle(\"Répartition de l'erreur renormalisée\", fontsize=14)\n",
    "plot_error(ax1, n=10)\n",
    "plot_error(ax2, n=1000)\n",
    "plt.show()\n",
    "# pour N = 10 la répartition de l'erreur ne semble pas vraiment gaussienne\n",
    "# pour N = 1000 le comportement semble gaussien"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a5b46ab-d911-4bd4-a94d-cea1cf217889",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "aa218f54-374f-4d2e-8773-8eff7162ab37",
   "metadata": {},
   "source": [
    "## Un premier exemple d'estimateur de Monte Carlo\n",
    "\n",
    "On va mettre en oeuvre un estimateur de Monte Carlo pour calculer\n",
    "\n",
    "$$\n",
    "  I(\\beta) = \\mathbf{E}[\\exp(\\beta G)] \\quad \n",
    "  \\text{où $G \\sim \\mathcal{N}(0,1)$ et $\\beta \\in \\mathbf{R}$}. \n",
    "$$\n",
    "\n",
    "La valeur exacte $I(\\beta) = \\exp(\\beta^2/2)$ est connue mais cet exemple permet d'illustrer l'importance des bornes de l'intervalle de confiance (et donc de l'estimation de la variance) dans une méthode de Monte Carlo. La seule valeur moyenne $I_n = \\frac{1}{n} \\sum_{k=1}^n X_k$ n'est pas suffisante pour déterminer $I$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "227b7a6d-1c9c-41c8-a15d-235c3a309ee7",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: fonction `monte_carlo`\n",
    "\n",
    "Ecrire une fonction `monte_carlo(sample, proba=0.95)` qui à partir d'un échantillon `sample` de réalisation indépendantes $(X_k)_{k=1,\\dots,n}$ renvoie un tuple qui contient: \n",
    "\n",
    "- la moyenne de l'estimateur Monte Carlo de $I = \\mathbf{E}[X]$,\n",
    "- l'estimateur de la variance asymptotique apparaissant dans le TCL,\n",
    "- les bornes inférieures et supérieures de l'intervale de confiance de niveau de probabilité `proba`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "728f1a52-f4b2-4c8e-8f0c-20f4094292db",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "def monte_carlo(sample, proba = 0.95):\n",
    "    \"\"\"\n",
    "    Computes the mean, variance, and a 95% confidence interval of a \n",
    "    given sample data set using the Monte Carlo method.\n",
    "    Parameters:\n",
    "    -----------\n",
    "    sample : array-like\n",
    "        The data set to be analyzed\n",
    "    proba : float, optional\n",
    "        The probability that the true mean of the population is \n",
    "        within the calculated interval. Default is 0.95\n",
    "    Returns:\n",
    "    --------\n",
    "    tuple : float\n",
    "        The mean, variance, lower bound of the 95% CI and upper bound of the 95% CI\n",
    "    \"\"\"\n",
    "    mean = np.mean(sample)\n",
    "    var = np.var(sample, ddof=1)\n",
    "    alpha = 1 - proba \n",
    "    quantile = stats.norm.ppf(1 - alpha/2)  # fonction quantile \n",
    "    ci_size = quantile * np.sqrt(var / sample.size)\n",
    "    return {\n",
    "        \"mean\": mean, \n",
    "        \"var\": var, \n",
    "        \"lower\": mean - ci_size, \n",
    "        \"upper\": mean + ci_size\n",
    "    }\n",
    "    #return (mean, var, mean - ci_size, mean + ci_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f1c949d-63c4-48f2-9523-29445c96a71e",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: premier exemple\n",
    "\n",
    "En utilisant la fonction `monte_carlo`, reproduire le tableau suivant où chaque ligne représente un résultat pour une valeur de $\\beta \\in \\{0.2, 0.5, 1, 2, 3, 5\\}$: \n",
    "\n",
    "- la première colonne est la valeur moyenne $I_n$,\n",
    "- la deuxième colonne l'estimateur de la variance,\n",
    "- les colonnes 3 et 4 sont les bornes inférieures et supérieurs de l'IC à 95%,\n",
    "- la colonne 5 contient la valeur exacte $\\mathbf{E}[\\exp(\\beta G)] = \\exp(\\beta^2/2)$.\n",
    "\n",
    "Ce tableau est obtenu pour $n = 1\\,000\\,000$. Comment interpréter ce tableau? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "69aa7e19-9d81-4ce9-9ccf-a93221f56bed",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>var</th>\n",
       "      <th>low</th>\n",
       "      <th>high</th>\n",
       "      <th>exact</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>1.020551</td>\n",
       "      <td>4.245536e-02</td>\n",
       "      <td>1.020147</td>\n",
       "      <td>1.020955</td>\n",
       "      <td>1.020201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>1.134027</td>\n",
       "      <td>3.650418e-01</td>\n",
       "      <td>1.132843</td>\n",
       "      <td>1.135212</td>\n",
       "      <td>1.133148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>1.651060</td>\n",
       "      <td>4.676691e+00</td>\n",
       "      <td>1.646821</td>\n",
       "      <td>1.655298</td>\n",
       "      <td>1.648721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>7.402685</td>\n",
       "      <td>2.379946e+03</td>\n",
       "      <td>7.307068</td>\n",
       "      <td>7.498301</td>\n",
       "      <td>7.389056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>87.915075</td>\n",
       "      <td>8.558333e+06</td>\n",
       "      <td>82.181273</td>\n",
       "      <td>93.648877</td>\n",
       "      <td>90.017131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5.0</th>\n",
       "      <td>121963.825619</td>\n",
       "      <td>6.439313e+14</td>\n",
       "      <td>72228.169429</td>\n",
       "      <td>171699.481809</td>\n",
       "      <td>268337.286521</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              mean           var           low           high          exact\n",
       "0.2       1.020551  4.245536e-02      1.020147       1.020955       1.020201\n",
       "0.5       1.134027  3.650418e-01      1.132843       1.135212       1.133148\n",
       "1.0       1.651060  4.676691e+00      1.646821       1.655298       1.648721\n",
       "2.0       7.402685  2.379946e+03      7.307068       7.498301       7.389056\n",
       "3.0      87.915075  8.558333e+06     82.181273      93.648877      90.017131\n",
       "5.0  121963.825619  6.439313e+14  72228.169429  171699.481809  268337.286521"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_pickle(\"data/first_df.pkl\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dbfea575-5725-4f50-b55c-8eed8907b553",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "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>mean</th>\n",
       "      <th>var</th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "      <th>exact</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>1.019915</td>\n",
       "      <td>4.251146e-02</td>\n",
       "      <td>1.019511</td>\n",
       "      <td>1.020319</td>\n",
       "      <td>1.020201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>1.132479</td>\n",
       "      <td>3.652511e-01</td>\n",
       "      <td>1.131294</td>\n",
       "      <td>1.133663</td>\n",
       "      <td>1.133148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>1.647759</td>\n",
       "      <td>4.681183e+00</td>\n",
       "      <td>1.643518</td>\n",
       "      <td>1.652000</td>\n",
       "      <td>1.648721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>7.396289</td>\n",
       "      <td>2.636496e+03</td>\n",
       "      <td>7.295651</td>\n",
       "      <td>7.496927</td>\n",
       "      <td>7.389056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>89.138017</td>\n",
       "      <td>1.533818e+07</td>\n",
       "      <td>81.462017</td>\n",
       "      <td>96.814018</td>\n",
       "      <td>90.017131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5.0</th>\n",
       "      <td>165252.929067</td>\n",
       "      <td>3.878368e+15</td>\n",
       "      <td>43193.151143</td>\n",
       "      <td>287312.706990</td>\n",
       "      <td>268337.286521</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              mean           var         lower          upper          exact\n",
       "0.2       1.019915  4.251146e-02      1.019511       1.020319       1.020201\n",
       "0.5       1.132479  3.652511e-01      1.131294       1.133663       1.133148\n",
       "1.0       1.647759  4.681183e+00      1.643518       1.652000       1.648721\n",
       "2.0       7.396289  2.636496e+03      7.295651       7.496927       7.389056\n",
       "3.0      89.138017  1.533818e+07     81.462017      96.814018      90.017131\n",
       "5.0  165252.929067  3.878368e+15  43193.151143  287312.706990  268337.286521"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = int(1e6)\n",
    "sample = rng.standard_normal(size=n)\n",
    "\n",
    "betas = [0.2, 0.5, 1, 2, 3, 5]\n",
    "result = [ monte_carlo(np.exp(beta * sample)) for beta in betas ]\n",
    "\n",
    "# results est une liste de tuple on peut le convertir en DataFrame \n",
    "# pour manipuler plus facilement ce résultat \n",
    "import pandas as pd\n",
    "res_df = pd.DataFrame(result, \n",
    "                      columns=[\"mean\", \"var\", \"lower\", \"upper\"], \n",
    "                      index=betas)\n",
    "res_df[\"exact\"] = np.exp(0.5 * np.array(betas)**2)\n",
    "res_df\n",
    "#res_df.to_pickle(\"data/first_df.pkl\")  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da8bbc68-33fb-47fb-9816-de3b4f2d6cbc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "048d17c1-5a98-4d72-aaae-5c7370165e87",
   "metadata": {},
   "source": [
    "## Option panier: un exemple multidimensionnel\n",
    "\n",
    "On considère $d \\ge 2$ actifs financiers dont la loi à l'instant $T > 0$ est modélisée par une loi log-normale c'est à dire \n",
    "\\begin{equation*}\n",
    "    \\forall i \\in \\{1,\\dots,d\\}, \\quad\n",
    "    S^i_T = S^i_0 \\exp\\Bigl( \\bigl(r-\\frac{\\sigma_i^2}{2}\\bigr) T + \\sigma_i \\sqrt{T} \\tilde G_i \\Bigr)\n",
    "\\end{equation*}\n",
    "où le vecteur $(\\tilde G_1,\\dots, \\tilde G_d)$ est gaussien centré de matrice de covariance $\\Sigma$ et les constantes $r > 0$, $\\sigma_i > 0$ sont fixées. Il s'agit d'actifs financiers $(S^i_t)_{t \\in [0,T]}$, $1 \\le i \\le d$, modélisés par un processus de Black-Scholes multidimensionnel. On introduit la matrice $L$ triangulaire inférieure obtenue par la décomposition de Cholesky de la matrice $\\Sigma = L L^\\top$. \n",
    "\n",
    "A l'aide de cette matrice $L$, on définit la fonction $\\Phi:\\mathbf{R}^d \\to \\mathbf{R}^d$ telle que \n",
    "\\begin{equation*}\n",
    "    (S^1_T, \\dots, S^d_T) = \\Phi(G_1, \\dots, G_d) \\quad \\text{ou encore} \\quad S^i_T = \\Phi_i(G_1, \\dots, G_d)\n",
    "\\end{equation*}\n",
    "où $(G_1, \\dots, G_d) \\sim \\mathcal{N}(0, I_d)$ (l'égalité précédente est à considérer en loi).\n",
    "\n",
    "On s'intéresse au prix d'une option européenne (aussi appelé produit dérivé européen) sur le panier de ces $d$ actifs financiers, c'est à dire qu'on veut calculer \n",
    "\\begin{equation*}\n",
    "    \\mathbf{E} \\bigl[ X \\bigr] %\\quad \\text{avec} \\quad g(x) = (x-K)_+ \\quad \\text{ou} \\quad g(x) = (K-x)_+ \n",
    "    \\quad \\text{avec} \\quad \n",
    "    X = \\biggl(\\frac{1}{d} \\sum_{i=1}^d S^i_T  - K\\biggr)_+.\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cce85a35-c93f-4b1e-9369-12ee4a6272f1",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: initialisation \n",
    "\n",
    "Définir les paramètres globaux $d = 10$, $T = 1$, $r = 0.01$, $S^i_0 =100$ (pour tous les actifs), $\\sigma_i = i / (2d)$ (on dit que certains actifs sont plus volatiles que d'autres) et la matrice de corrélation $\\Sigma$ définie par $\\Sigma_{i,i} = 1$ et $\\Sigma_{i,j} = \\rho \\in [0,1]$ pour $i \\neq j$, avec $\\rho = 0.2$.\n",
    "\n",
    "Initialiser la matrice $L$ en utilisant la fonction `np.linalg.cholesky`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "af189370-6c45-43e1-ae02-75ea07615de5",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "d = 10\n",
    "T = 1\n",
    "r = 0.01\n",
    "S0 = np.full(d, 100)\n",
    "sigma = np.arange(1,d+1)/(2*d)\n",
    "mu = r - 0.5*sigma**2\n",
    "rho = 0.2\n",
    "correl = np.full((d,d), rho) + (1-rho)*np.eye(d) #ou np.diag(np.full(d, 1-rho))\n",
    "mat_L = np.linalg.cholesky(correl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "64f3b0bf-e33a-4073-9d13-5182866bc93f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2],\n",
       "       [0.2, 1. , 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2],\n",
       "       [0.2, 0.2, 1. , 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2],\n",
       "       [0.2, 0.2, 0.2, 1. , 0.2, 0.2, 0.2, 0.2, 0.2, 0.2],\n",
       "       [0.2, 0.2, 0.2, 0.2, 1. , 0.2, 0.2, 0.2, 0.2, 0.2],\n",
       "       [0.2, 0.2, 0.2, 0.2, 0.2, 1. , 0.2, 0.2, 0.2, 0.2],\n",
       "       [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 1. , 0.2, 0.2, 0.2],\n",
       "       [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 1. , 0.2, 0.2],\n",
       "       [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 1. , 0.2],\n",
       "       [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 1. ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e4cd2f0d-2f50-41e9-b73b-27921d69e560",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.9797959 , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.96609178, 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.95618289, 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.11952286, 0.9486833 ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.11952286, 0.10540926,\n",
       "        0.94280904, 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.11952286, 0.10540926,\n",
       "        0.0942809 , 0.93808315, 0.        , 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.11952286, 0.10540926,\n",
       "        0.0942809 , 0.08528029, 0.93419873, 0.        , 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.11952286, 0.10540926,\n",
       "        0.0942809 , 0.08528029, 0.07784989, 0.93094934, 0.        ],\n",
       "       [0.2       , 0.16329932, 0.13801311, 0.11952286, 0.10540926,\n",
       "        0.0942809 , 0.08528029, 0.07784989, 0.07161149, 0.92819096]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat_L"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8427fa3d-b0d1-402e-a8dc-b1e32ae620ec",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: simulation d'un échantillon d'actifs\n",
    "\n",
    "Définir la fonction python `phi` qui transforme le vecteur $(G_1, \\dots, G_d)$ en un vecteur $(S_T^1,\\dots, S_T^d)$ (tous les paramètres sont des variables globales pour simplifier l'écriture du code). L'appel suivant doit fonctionner \n",
    "```\n",
    "G = rng.standard_normal(size=d)\n",
    "phi(G)\n",
    "```\n",
    "Si on veut implémenter un estimateur Monte Carlo il faut travailler avec des échantillons _i.i.d._ $(S^{(j)}_T)_{j=1,\\dots,n}$ où $S^{(j)}_T = \\big(S_T^{(j),1}, \\dots, S_T^{(j),d}\\big) \\in \\mathbf{R}^d$. Modifier votre fonction `phi` pour création un tel échantillon à partir de l'appel suivant: \n",
    "```\n",
    "sample_G = rng.standard_normal(size=(d, n))\n",
    "phi(sample_G)\n",
    "```\n",
    "(il faut utiliser la technique du broadcasting en `numpy`, c'est très important à connaitre en pratique)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9808a1bf-1553-4b35-a71d-1ce22de478cc",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.08371475 116.17333953 140.05911369  92.36778047 102.73992594\n",
      "  65.08890654 113.42440183  99.64079311  70.62603938 161.43417037]\n",
      "[[108.66599934  96.25031308 110.06319968 ...  99.0937169  108.29719718\n",
      "  109.96403182]\n",
      " [103.90691598 110.15752805 103.84158588 ...  93.51912781 113.84788509\n",
      "  110.0242026 ]\n",
      " [ 78.35547474  91.62714862 122.72499603 ...  87.61071647 121.2718228\n",
      "  105.30590879]\n",
      " ...\n",
      " [ 96.44719072  73.68389103  94.13258892 ... 152.74164559 107.51750385\n",
      "  135.87642981]\n",
      " [ 32.62381453  33.40193876  85.20275394 ...  61.51557622 311.07708964\n",
      "  101.63745188]\n",
      " [170.41591196  69.60820817 109.20990405 ...  90.81371251  80.59042776\n",
      "  105.49755197]]\n"
     ]
    }
   ],
   "source": [
    "# première version\n",
    "def phi(G): \n",
    "    ST = S0 * np.exp(mu * T + sigma * np.sqrt(T) * mat_L @ G)\n",
    "    return ST\n",
    "\n",
    "G = rng.standard_normal(size=d)\n",
    "print(phi(G))\n",
    "\n",
    "# deuxième version pour obtenir un échantillon de taille `n`\n",
    "def phi(sample_G): \n",
    "    sample_ST = S0[:,np.newaxis] * np.exp(mu[:,np.newaxis] * T \n",
    "                + sigma[:,np.newaxis] * np.sqrt(T) * mat_L @ sample_G)\n",
    "    return sample_ST\n",
    "\n",
    "n = 1000\n",
    "sample_G = rng.standard_normal(size=(d, n))\n",
    "print(phi(sample_G))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d8ff622-af28-4b12-aba9-92a1b3b422fa",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: estimateur Monte Carlo \n",
    "\n",
    "Définir une fonction $\\psi: \\mathbf{R}^d \\times \\mathbf{R}_+ \\to \\mathbf{R}_+$ telle que\n",
    "\\begin{equation*}\n",
    "  \\psi(G_1, \\dots, G_d, K) = \n",
    "  \\biggl(\\frac{1}{d} \\sum_{i=1}^d \\Phi_i(G_1, \\dots, G_d) - K\\biggr)_+\n",
    "\\end{equation*}\n",
    "dans une fonction `python` appelée `psi`. Cette fonction doit fonctionner avec un échantillon $(G^{(j)}_1, \\dots, G^{(j)}_d)_{j=1,\\dots,n}$.  \n",
    "Ecrire et programmer l'estimateur de Monte Carlo pour estimer la quantité $\\mathbf{E}[X] = \\mathbf{E}[\\psi(G_1, \\dots, G_d, K)]$ où $(G_1, \\dots, G_d) \\sim \\mathcal{N}(0, I_d)$.  \n",
    "\n",
    "Pour différentes valeur de $K \\in \\{80,90,100,110,120\\}$ et $n = 100\\,000$ vous devez obtenir le tableau suivant: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fbf3346e-91e5-4cbe-9c48-599ed101d177",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\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>mean</th>\n",
       "      <th>var</th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>21.394471</td>\n",
       "      <td>228.318772</td>\n",
       "      <td>21.300818</td>\n",
       "      <td>21.488123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>12.860460</td>\n",
       "      <td>181.187947</td>\n",
       "      <td>12.777032</td>\n",
       "      <td>12.943889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>6.655165</td>\n",
       "      <td>111.553749</td>\n",
       "      <td>6.589702</td>\n",
       "      <td>6.720627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>2.998650</td>\n",
       "      <td>54.132985</td>\n",
       "      <td>2.953049</td>\n",
       "      <td>3.044252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>120</th>\n",
       "      <td>1.204158</td>\n",
       "      <td>21.976278</td>\n",
       "      <td>1.175102</td>\n",
       "      <td>1.233213</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean         var      lower      upper\n",
       "80   21.394471  228.318772  21.300818  21.488123\n",
       "90   12.860460  181.187947  12.777032  12.943889\n",
       "100   6.655165  111.553749   6.589702   6.720627\n",
       "110   2.998650   54.132985   2.953049   3.044252\n",
       "120   1.204158   21.976278   1.175102   1.233213"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_pickle(\"data/basket_mc.pkl\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "be6c113a-87f4-47cb-813b-d0dabf1bbb18",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>mean</th>\n",
       "      <th>var</th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>21.303890</td>\n",
       "      <td>228.154859</td>\n",
       "      <td>21.274285</td>\n",
       "      <td>21.333495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>12.776736</td>\n",
       "      <td>181.047917</td>\n",
       "      <td>12.750364</td>\n",
       "      <td>12.803108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>6.594640</td>\n",
       "      <td>111.543095</td>\n",
       "      <td>6.573940</td>\n",
       "      <td>6.615340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>2.969353</td>\n",
       "      <td>54.423565</td>\n",
       "      <td>2.954894</td>\n",
       "      <td>2.983812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>120</th>\n",
       "      <td>1.200447</td>\n",
       "      <td>22.437365</td>\n",
       "      <td>1.191163</td>\n",
       "      <td>1.209731</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean         var      lower      upper\n",
       "80   21.303890  228.154859  21.274285  21.333495\n",
       "90   12.776736  181.047917  12.750364  12.803108\n",
       "100   6.594640  111.543095   6.573940   6.615340\n",
       "110   2.969353   54.423565   2.954894   2.983812\n",
       "120   1.200447   22.437365   1.191163   1.209731"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def psi(sample_G, K): \n",
    "    return np.maximum(phi(sample_G).mean(axis=0) - K, 0)\n",
    "\n",
    "n = int(1e6)\n",
    "sample_G = rng.standard_normal(size=(d, n))\n",
    "Ks = [80, 90, 100, 110, 120]\n",
    "result = [ monte_carlo(psi(sample_G, K)) for K in Ks ]\n",
    "df_mc = pd.DataFrame(result, index=Ks)\n",
    "#df_mc = pd.DataFrame(result, \n",
    "#                         columns=['mean', 'var', 'lower', 'upper'], \n",
    "#                         index=Ks)\n",
    "df_mc\n",
    "#df_mc.to_pickle('data/basket_mc.pkl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "469f3249-caf3-46a0-8fea-671a2887a908",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: monte-carlo adaptatif \n",
    "\n",
    "Ecrire une fonction `monte_carlo_adaptive` pour calculer le prix à une précision $\\epsilon > 0$ fixée (telle que la taille de l'IC à un niveau de confiance donné soit plus petite que $\\epsilon$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "de51fd8b-dbc3-48f6-95cb-38a30852955a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "from time import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f89c9933-5a89-40cc-aa4d-2591ab0b0b5e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "def monte_carlo_adaptive(get_sample: callable, epsilon: float, \n",
    "                         batch_size: int=10000, proba: float=0.95):\n",
    "    # on récupère un sample de taille batch_size\n",
    "    sample = get_sample(batch_size) \n",
    "\n",
    "    start = time()\n",
    "    # on fait une boucle en appelant monte_carlo pour atteindre epsilon (pas optimal)\n",
    "    r_MC = monte_carlo(sample, proba)\n",
    "    ci_range = r_MC[\"upper\"] - r_MC[\"lower\"]\n",
    "    size = batch_size \n",
    "    while ci_range >= epsilon: \n",
    "        # attention l'approche n'est pas optimale: la complexité n'est plus linéaire !!! \n",
    "        sample = np.hstack([sample, get_sample(batch_size)]) # non optimal \n",
    "        r_MC = monte_carlo(sample, proba)  # car reutilisation de ce bout de code \n",
    "        ci_range = r_MC[\"upper\"] - r_MC[\"lower\"]\n",
    "        size += batch_size  \n",
    "    stop = time()\n",
    "    \n",
    "    result = r_MC\n",
    "    result[\"size\"] = size \n",
    "    result[\"time\"] = stop - start\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "fbb85599-c5a3-4c21-95f3-bdfc516902cf",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "def get_payoffs_K(batch_size: int, K: float): \n",
    "    sample_G = rng.standard_normal(size=(d, batch_size))\n",
    "    return psi(sample_G, K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "cbfe860f-a034-49c8-b276-fdb744639525",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "Ks = [80, 90, 100, 110, 120]\n",
    "result = [ monte_carlo_adaptive(\n",
    "            lambda size: get_payoffs_K(size, K),  # argument get_sample\n",
    "            epsilon=0.01, batch_size=100000\n",
    "            ) for K in Ks ]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "eac5939f-ac90-444c-9d86-7af99bfb6238",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "correction"
    ]
   },
   "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>mean</th>\n",
       "      <th>var</th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "      <th>size</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>21.298602</td>\n",
       "      <td>228.364732</td>\n",
       "      <td>21.293602</td>\n",
       "      <td>21.303601</td>\n",
       "      <td>35100000</td>\n",
       "      <td>24.682171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>12.776653</td>\n",
       "      <td>181.060717</td>\n",
       "      <td>12.771660</td>\n",
       "      <td>12.781646</td>\n",
       "      <td>27900000</td>\n",
       "      <td>16.515140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>6.591118</td>\n",
       "      <td>111.598646</td>\n",
       "      <td>6.586125</td>\n",
       "      <td>6.596110</td>\n",
       "      <td>17200000</td>\n",
       "      <td>8.081024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>2.969548</td>\n",
       "      <td>54.450206</td>\n",
       "      <td>2.964557</td>\n",
       "      <td>2.974538</td>\n",
       "      <td>8400000</td>\n",
       "      <td>2.450883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>120</th>\n",
       "      <td>1.196421</td>\n",
       "      <td>22.447703</td>\n",
       "      <td>1.191457</td>\n",
       "      <td>1.201385</td>\n",
       "      <td>3500000</td>\n",
       "      <td>0.657661</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean         var      lower      upper      size       time\n",
       "80   21.298602  228.364732  21.293602  21.303601  35100000  24.682171\n",
       "90   12.776653  181.060717  12.771660  12.781646  27900000  16.515140\n",
       "100   6.591118  111.598646   6.586125   6.596110  17200000   8.081024\n",
       "110   2.969548   54.450206   2.964557   2.974538   8400000   2.450883\n",
       "120   1.196421   22.447703   1.191457   1.201385   3500000   0.657661"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(result, index=Ks)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9416f9fa-c4e0-4597-8d9e-1dd3a872653f",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: variables antithétiques \n",
    "\n",
    "Sur le même modèle que précédemment, implémenter la méthode de Monte Carlo avec réduction de variance par variables antithétiques c'est à dire basée sur la représentation: \n",
    "\\begin{equation*}\n",
    "    \\mathbf{E}[X] = \\mathbf{E} \\Big[ \\frac{1}{2} \\bigl( \\psi(G_1, \\dots, G_d, K) + \\psi(-G_1, \\dots, -G_d, K) \\bigr) \\Big]\n",
    "\\end{equation*}\n",
    "Calculer le ratio de variance (variance de la méthode naïve divisée par variance par variables antithétiques) pour les différentes valeurs de $K$.  \n",
    "Que signifie ce ratio de variance?  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fd72a55f-a5e5-46c7-9142-1f85383696d0",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "sample_G = rng.standard_normal(size=(d, n))\n",
    "Ks = [80, 90, 100, 110, 120]\n",
    "result = []\n",
    "for K in Ks:\n",
    "    sample = 0.5 * (psi(sample_G, K) + psi(-sample_G, K))\n",
    "    result.append(monte_carlo(sample))\n",
    "df_antith = pd.DataFrame(result, index=Ks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "41ac89fe-c3db-42f7-b58d-1a5a596dd9b1",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80     15.922708\n",
       "90      6.957182\n",
       "100     3.262194\n",
       "110     2.385265\n",
       "120     2.130627\n",
       "Name: var, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# le ratio des variances pour les différentes valeurs de K\n",
    "df_mc[\"var\"] / df_antith[\"var\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "806f8959-f831-43da-ae57-cbb36e2ee66a",
   "metadata": {},
   "source": [
    "## Option panier: une variable de contrôle \n",
    "\n",
    "Dans le cas de la dimension 1 ($d=1$), le prix est donnée par une formule fermée, on appelle cette formule la formule de Black-Scholes. Pour une option Basket (en dimension $d \\ge 2$) on approche le prix par Monte Carlo mais on peut utiliser des approximations pour construire un problème unidimensionnel proche du produit Basket. Ces approximations servent de variables de contrôles: **on ne rajoute pas une erreur, on retire de la variance**.\n",
    "\n",
    "On rappelle que, en posant $\\mu_i = r - \\frac{1}{2}\\sigma_i^2$,\n",
    "\\begin{equation*}\n",
    "    X = \\biggl(\\frac{1}{d} \\sum_{i=1}^d S^i_0 e^{\\mu_i T + \\sigma_i \\sqrt{T}  \\tilde G_i}  - K\\biggr)_+\n",
    "\\end{equation*}\n",
    "et en introduisant $a^i_0 = \\frac{S^i_0}{\\sum_{j=1}^d S^j_0}$ (t.q. $\\sum a^i_0 = 1$) et $\\bar S_0 = \\frac{1}{d} \\sum_{i=1}^d S^i_0$ on a \n",
    "\\begin{equation*}\n",
    "    X = \\biggl(\\bar S_0 \\sum_{i=1}^d a^i_0 e^{\\mu_i T + \\sigma_i \\sqrt{T}  \\tilde G_i}  - K\\biggr)_+.\n",
    "\\end{equation*}\n",
    "La variable de contrôle proposée est obtenue en échangeant l'exponentielle et la moyenne pondérée par les poids $\\big(a^i_0\\big)_{i=1,\\dots,d}$:\n",
    "\\begin{equation*}\n",
    "    Y = \\bigl(\\bar S_0 e^Z  - K\\bigr)_+\n",
    "    \\quad \\text{avec} \\quad \n",
    "    Z = \\sum_{i=1}^d a^i_0 \\big(\\mu_i T + \\sigma_i \\sqrt{T}  \\tilde G_i\\big) \n",
    "\\end{equation*}\n",
    "La variable aléatoire $Z$ suit une loi gaussienne $Z \\sim \\mathcal{N}(m T, s^2 T)$ avec\n",
    "\\begin{equation*}\n",
    "    m = \\sum_{i=1}^d a^i_0 \\mu_i\n",
    "    \\quad \\text{et} \\quad\n",
    "    s^2 = \\sum_{j=1}^d \\Big( \\sum_{i=1}^d a^i_0 \\sigma_i L_{ij} \\Big)^2. \n",
    "\\end{equation*}\n",
    "Ainsi l'espérance de la variable de contrôle $Y$ est connue par la formule de Black-Scholes, car elle correspond au prix d'un call de strike $K$ d'un actif Black-Scholes de dimension 1, de valeur initiale $\\bar S_0$, de taux $\\rho = m+\\frac{1}{2} s^2$ et de volatilité $s$ (à un facteur d'actualisation près... attention à ça). On a donc \n",
    "\\begin{equation*}\n",
    "    e^{-\\rho T} \\mathbf{E} \\big[ Y \\big] = P_{\\text{BS}}\\big(\\bar S_0, \\rho, s, T, K\\big),\n",
    "\\end{equation*}\n",
    "où \n",
    "\\begin{equation*}\n",
    "    P_{\\text{BS}}\\big(x, r, \\sigma, T, K\\big) = x F_{\\mathcal{N}(0,1)}(d_1) - K e^{-r T} F_{\\mathcal{N}(0,1)}(d_2),\n",
    "\\end{equation*}\n",
    "avec $F_{\\mathcal{N}(0,1)}$ est la fonction de répartition de la loi normale centrée réduite et  la notation \n",
    "\\begin{equation*}\n",
    "    d_1 = \\frac{1}{\\sigma \\sqrt{T}} \\Big( \\log\\big( \\frac{x}{K} \\big) \n",
    "    + \\big(r + \\frac{\\sigma^2}{2}\\big) T \\Big)\n",
    "    \\quad \\text{et} \\quad\n",
    "    d_2 = d_1 - \\sigma \\sqrt{T}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47e5e558-f825-406d-8175-7f6cb8c427e0",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: préliminaires pour la variable de contrôle\n",
    "\n",
    "- Définir la fonction `price_call_BS` qui code la fonction $P_{\\text{BS}}\\big(x, r, \\sigma, T, K\\big)$ définie ci-dessus.\n",
    "- Initialiser les paramètres $\\bar S_0$, $(a^i_0)_{i=1,\\dots,d}$, $m$, $s^2$ et $\\rho$.\n",
    "- Calculer $\\mathbf{E}[Y]$ par la formule fermée.\n",
    "- Calculer $\\mathbf{E}[Y]$ par un estimateur Monte Carlo à partir de réalisations de $( G_1^{(j)}, \\dots,  G_d^{(j)})$, $j \\in \\{1, \\dots, n\\}$.\n",
    "- Vérifier que tout est cohérent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5b55908f-cdbe-490f-913f-6caf13cd8b5c",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "def price_call_BS(x, r, sigma, T, K):\n",
    "    d1 = (np.log(x / K) + T * (r + 0.5*sigma**2)) / (sigma * np.sqrt(T))\n",
    "    d2 = d1 - sigma * np.sqrt(T)\n",
    "    return x * stats.norm.cdf(d1) - K * np.exp(-r * T) * stats.norm.cdf(d2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a02445f2-d153-4367-b35d-9fa642fc8c56",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "barS0 = S0.mean()   # ou np.mean(S0) \n",
    "a = S0 / S0.sum()   # np.sum(S0)\n",
    "m = (a * (r - 0.5*sigma**2)).sum()\n",
    "s2 = (((a * sigma).T @ mat_L)**2).sum()\n",
    "rho = m + 0.5*s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0a047ccc-2041-41c0-964c-783ba114f651",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.022825000000000005)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5d6c6dd5-4501-40b3-989c-0417d3912b36",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "c1754c29-e95a-4a2f-897b-6b5da41c2252",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True value: 4.7166246434390695\n"
     ]
    }
   ],
   "source": [
    "# calcul par formule fermée\n",
    "Y_mean = np.exp(rho*T) * price_call_BS(barS0, rho, np.sqrt(s2), T=T, K=K)\n",
    "print(\"True value:\", Y_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "0a96c859-03b5-438f-9f9b-81f0489160ee",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mean': np.float64(4.715366150094408),\n",
       " 'var': np.float64(72.98410535651907),\n",
       " 'lower': np.float64(4.662416604742982),\n",
       " 'upper': np.float64(4.768315695445835)}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calcul par Monte Carlo\n",
    "n = int(1e5)\n",
    "sample_G = rng.standard_normal(size=(d, n))\n",
    "Z = np.sum(a[:,None] * (m*T + sigma[:,None] * np.sqrt(T) * mat_L @ sample_G),\n",
    "           axis = 0)\n",
    "Y = np.maximum(S0.mean() * np.exp(Z) - K, 0) \n",
    "monte_carlo(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60e52cfa-01e9-451c-93e0-9a3a4d900485",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: MC avec variable de contrôle\n",
    "\n",
    "Implémenter l'estimateur de Monte Carlo avec variable de contrôle pour le calcul de $\\mathbf{E}[X]$ c'est à dire \n",
    "\\begin{equation*}\n",
    "    \\mathbf{E}\\big[ X \\big] = \\mathbf{E} \\big[\\psi(G_1,\\dots,G_d,K) - (Y - \\mathbf{E}[Y]) \\big],\n",
    "\\end{equation*}\n",
    "où $Y$ est la variable de contrôle introduite précédemment et $\\mathbf{E}[Y]$ est calculée par la formule fermée.  \n",
    "Comparer les ratios de variance pour les différentes valeurs de $K$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ffac1f49-7162-42bd-8e97-169f74aa99f0",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "Ks = [80, 90, 100, 110, 120]\n",
    "result = []\n",
    "for K in Ks:\n",
    "    Z = np.sum(a[:,None] * (m*T + sigma[:,None]*np.sqrt(T)*mat_L@sample_G), \n",
    "               axis = 0)\n",
    "    Y = np.maximum(S0.mean() * np.exp(Z) - K, 0) \n",
    "    Y_mean = np.exp(rho*T) * price_call_BS(barS0, rho, np.sqrt(s2), T=T, K=K)\n",
    "    control_variate = Y - Y_mean # variable centrée \n",
    "    sample = psi(sample_G, K) - control_variate\n",
    "    result.append(monte_carlo(sample))\n",
    "\n",
    "#df_cv = pd.DataFrame(result, \n",
    "#                     columns=['mean', 'var', 'lower', 'upper'], \n",
    "#                     index=Ks)\n",
    "df_cv = pd.DataFrame(result, index=Ks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "0eb4c99b-b390-4506-ae08-a2ce548eb834",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80     35.048882\n",
       "90     23.594268\n",
       "100    14.064549\n",
       "110     8.333556\n",
       "120     5.065413\n",
       "Name: var, dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# le ratio des variances pour les différentes valeurs de K\n",
    "df_mc[\"var\"] / df_cv[\"var\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "938c7b4f-a901-43f6-ab76-6f34353dbd39",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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