Modèles_de_Bachelier_et_Black_Scholes_en_Python.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t3DET0KH5WjI"
      },
      "source": [
        "Ce notebook couvre les modèles de tarification d'options tels que le modèle de Bachelier et le modèle de Black-Scholes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CBu9c2eD6AYe"
      },
      "source": [
        "# Fonctions Black-Scholes\n",
        "- Prix de l'option d'achat (call) et de vente (put) selon Black-Scholes\n",
        "- Fonctions objectif pour trouver la volatilité\n",
        "- Fonction pour vega, la dérivée du prix de l'option par rapport à la volatilité\n",
        "\n",
        "Le prix d'un call selon Black-Scholes est donné par,\n",
        "$$C = \\Phi(d_1) S - \\Phi(d_2) K e^{-r t},$$\n",
        "et le prix d'un put par,\n",
        "$$P = \\Phi(-d_2)e_{-rt} - \\Phi(-d_1)S,$$\n",
        "où\n",
        "$$d_1 = \\frac{1}{\\sigma \\sqrt{t}} \\left[ \\ln\\left(\\frac{S}{K}\\right) + \\left(r + \\frac{\\sigma.^2}{2}\\right) t\\right],$$\n",
        "et\n",
        "$$d_2 = d_1 - \\sigma \\sqrt{t}.$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cDaZY0vQ6RPW"
      },
      "source": [
        "Cette section présente les équations du modèle de Black-Scholes pour calculer le prix des options d'achat (call) et de vente (put). Les équations utilisent divers paramètres tels que le prix du sous-jacent (S), le prix d'exercice (K), le taux d'intérêt sans risque (r), la volatilité (σ), et le temps jusqu'à l'expiration (t)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CbCNuinG6px0"
      },
      "source": [
        "### Importation des bibliothèques"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "UPtndcnq20E-"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "from sympy import Symbol, diff, erf, sqrt, init_printing, ln, exp, diff, pi\n",
        "\n",
        "import seaborn as sns\n",
        "sns.set()\n",
        "\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p1I1C1GZ7K1e"
      },
      "source": [
        "On importe les bibliothèques nécessaires pour les calculs et la visualisation des données. numpy est utilisé pour les opérations mathématiques, matplotlib.pyplot pour la visualisation des données, et scipy.stats pour les fonctions statistiques. SymPy est utilisé pour les calculs symboliques et l'affichage de belles expressions mathématiques."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "idPtRM4D7a-b"
      },
      "source": [
        "### Fonctions Black-Scholes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "8nfhT9d-8FIo"
      },
      "outputs": [],
      "source": [
        "def call_price(sigma, S, K, r, t):\n",
        "    d1 = np.multiply( 1. / sigma * np.divide(1., np.sqrt(t)),\n",
        "        np.log(S/K) + (r + sigma**2 / 2.) * t  )\n",
        "    d2 = d1 - sigma * np.sqrt(t)\n",
        "\n",
        "    C = np.multiply(S, norm.cdf(d1)) - \\\n",
        "        np.multiply(norm.cdf(d2) * K, np.exp(-r * t))\n",
        "    return C, d1, d2\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZRYn-gSB8TCP"
      },
      "source": [
        "Cette fonction calcule le prix d'une option d'achat (call option) en utilisant la formule Black-Scholes. Les paramètres sont :\n",
        "<br><br>\n",
        "σ: Volatilité du sous-jacent <br>\n",
        "S: Prix du sous-jacent <br>\n",
        "K: Prix d'exercice de l'option <br>\n",
        "r: Taux d'intérêt sans risque <br>\n",
        "t: Temps jusqu'à l'expiration <br>\n",
        "\n",
        "Les variables intermédiaires d1 et d2 sont calculées comme spécifié dans la formule Black-Scholes. Enfin, le prix du call (C) est calculé en utilisant ces deux variables et renvoyé avec d1 et d2."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "7hFiG8ta9LtE"
      },
      "outputs": [],
      "source": [
        "def put_price(sigma, S, K, r, t):\n",
        "    d1 = np.multiply( 1. / sigma * np.divide(1., np.sqrt(t)),\n",
        "        np.log(S/K) + (r + sigma**2 / 2.) * t  )\n",
        "    d2 = d1 - sigma * np.sqrt(t)\n",
        "\n",
        "    P = -np.multiply(S, norm.cdf(-d1)) + \\\n",
        "        np.multiply(norm.cdf(-d2) * K, np.exp(-r * t))\n",
        "    return P\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J1Y5LQnf9LiY"
      },
      "source": [
        "Semblable à call_price, cette fonction calcule le prix d'une option de vente (put option) avec la même logique et les mêmes paramètres, mais utilise une formule différente pour le calcul final du prix de l'option de vente (P)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "GCxnUXu-9LQY"
      },
      "outputs": [],
      "source": [
        "def call_objective_function(sigma, args):\n",
        "    S = args[0]\n",
        "    K = args[1]\n",
        "    r = args[2]\n",
        "    t = args[3]\n",
        "    price = args[4]\n",
        "\n",
        "    return call_price(sigma, S, K, r, t) - price\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AHJh7BDT9K-G"
      },
      "source": [
        "Cette fonction prend un ensemble d'arguments ***args*** et une volatilité σ, et renvoie la différence entre le prix du call calculé avec ***call_price*** et un prix cible ***price***. Cela peut être utilisé pour calibrer le modèle en ajustant σ pour minimiser cette fonction objective, c'est-à-dire trouver la volatilité implicite."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "UwaGd4Rp9Ks4"
      },
      "outputs": [],
      "source": [
        "def put_objective_function(sigma, args):\n",
        "    S = args[0]\n",
        "    K = args[1]\n",
        "    r = args[2]\n",
        "    t = args[3]\n",
        "    price = args[4]\n",
        "\n",
        "    return put_price(sigma, S, K, r, t) - price\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pgdxHVLI9Kde"
      },
      "source": [
        "Semblable à ***call_objective_function***, mais pour les options de vente. Elle renvoie la différence entre le prix de l'option de vente calculé et un prix cible.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "eVZBsop98Pwj"
      },
      "outputs": [],
      "source": [
        "def calculate_vega(sigma, args):\n",
        "    S = args[0]\n",
        "    K = args[1]\n",
        "    r = args[2]\n",
        "    t = args[3]\n",
        "\n",
        "    d1 = np.multiply( 1. / sigma * np.divide(1., np.sqrt(t)),\n",
        "        np.log(S/K) + (r + sigma**2 / 2.) * t  )\n",
        "    d2 = d1 - sigma * np.sqrt(t)\n",
        "\n",
        "    return S * norm.pdf(d1) * np.sqrt(t)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7yqYV72_8QK7"
      },
      "source": [
        "Vega mesure la sensibilité du prix d'une option aux changements de volatilité du sous-jacent. Cette fonction calcule et renvoie Vega en utilisant les paramètres d'entrée args et la volatilité\n",
        "<br>\n",
        "σ. Vega est utilisé dans le cadre de la gestion du risque de volatilité d'un portefeuille d'options et est particulièrement utile lors du trading de volatilité."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2BPWjhig_IeK"
      },
      "source": [
        "Chacune de ces fonctions joue un rôle crucial dans le calcul et l'analyse des options en utilisant le modèle de Black-Scholes, en permettant de calculer les prix des options et de calibrer le modèle à des prix de marché."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8QAlMII420FG"
      },
      "source": [
        "# Modèle Bachelier\n",
        "\n",
        "$$\n",
        "C = e^{-rt} \\left(Se^{rt}-K\\right)\n",
        "\\Phi\\left( \\frac{Se^{rt}-K}{ \\sqrt{\\frac{\\sigma^2}{2r}(e^{2rt} - 1)}} \\right) +\n",
        "e^{-rt}\\sqrt{\\frac{\\sigma^2}{2r}(e^{2rt} - 1)}\n",
        "\\phi\\left(  \\frac{Se^{rt}-K}{ \\sqrt{\\frac{\\sigma^2}{2r}(e^{2rt} - 1)}} \\right)\n",
        "$$\n",
        "\n",
        "La fonction ***bachelier*** calcule le prix d'une option d'achat"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "d2MG1L-U20FH"
      },
      "outputs": [],
      "source": [
        "def bachelier(sigma, S, K, r, t):\n",
        "    d = (S * np.exp(r*t) - K) / np.sqrt(sigma**2/(2 * r) * (np.exp(2*r*t)-1) )\n",
        "\n",
        "    C = np.exp(-r * t) * (S * np.exp(r * t) - K) * norm.cdf(d) + \\\n",
        "        np.exp(-r * t) * np.sqrt(sigma**2/(2*r) * (np.exp(2*r*t)-1) ) * norm.pdf(d)\n",
        "\n",
        "    return C"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gbGmqrLA20FH"
      },
      "source": [
        "# Visualisation des modèles"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "id": "DcrKLH7820FI",
        "outputId": "20607a69-bf4d-4c53-b768-29d1503b1a43"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_7798/1240337607.py:13: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k\" (-> color=(0.1, 0.1, 0.1, 1)). The keyword argument will take precedence.\n",
            "  plt.plot(S, C_bs, 'k', label='Black-Scholes', color='red')\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Prix du call ($)')"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "t = 30 / 365    # Temps jusqu'à l'expiration\n",
        "sigma = 0.30    # Volatilité implicite de Black-Scholes\n",
        "K = 105         # Prix d'exercice\n",
        "r = 0.01        # Taux sans risque\n",
        "\n",
        "S = np.linspace(90, 110, 100)    # Laissons notre prix de l'action varier entre 90$ et 110$\n",
        "\n",
        "# Calculons les prix des options selon les deux modèles\n",
        "C_bs, d1, d2 = call_price(sigma, S, K, r, t)\n",
        "C_ba = bachelier(sigma * S, S, K, r, t)\n",
        "\n",
        "# Visualiton les résultats\n",
        "plt.plot(S, C_bs, 'k', label='Black-Scholes', color='red')\n",
        "plt.plot(S, C_ba, 'b.', label='Bachelier')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlabel('Prix de l’action (4)')\n",
        "plt.ylabel('Prix du call ($)')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UPNkZSoSB52h"
      },
      "source": [
        "Calculons $\\Delta$ pour le modèle de Bachelier en utilisant une technique de différence finie pour prendre la dérivée. Faisons cela pour un call à la monnaie avec un prix d'exercice de \\(105\\). Nous conserverons les autres paramètres tels que mentionnés ci-dessus.\n",
        "\n",
        "Nous utiliserons,\n",
        "$$\\frac{dr}{dx} \\approx \\frac{f(x + \\epsilon) + f(x)}{\\epsilon}$$\n",
        "comme notre approximation pour la dérivée. <br><br>\n",
        "La méthode des différences finies est utilisée pour approximer la dérivée du prix de l'option par rapport au prix de l'actif sous-jacent."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tyNwFdiN20FK",
        "outputId": "7b171714-5acb-436b-f3f1-85bbca30fab2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Delta BS =  0.520958769045928\n",
            "Delta BA =  0.5038124020195767\n"
          ]
        }
      ],
      "source": [
        "t = 30 / 365\n",
        "sigma = 0.30\n",
        "K = 105\n",
        "r = 0.01\n",
        "S = 105\n",
        "\n",
        "# Pour Black-Scholes, nous avons une formule pour delta : Delta = norm.cdf(d1)\n",
        "C_bs, d1, d2 = call_price(sigma, S, K, r, t)\n",
        "Delta_bs = norm.cdf(d1)\n",
        "print('Delta BS = ', Delta_bs)\n",
        "\n",
        "# Définissons epsilon comme un petit nombre\n",
        "epsilon = 1e-6\n",
        "\n",
        "# Calculons les prix des calls\n",
        "C1_ba = bachelier(sigma * S, S, K, r, t)\n",
        "C2_ba = bachelier(sigma * S, S + epsilon, K, r, t)\n",
        "\n",
        "# Estimons Delta\n",
        "Delta_ba = (C2_ba - C1_ba) / epsilon\n",
        "print('Delta BA = ', Delta_ba)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u3DCvoxDCxTs"
      },
      "source": [
        "Voici notre code pour la méthode de Newton pour la recherche de racine.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "3S6x79M_20FL"
      },
      "outputs": [],
      "source": [
        "def newtons_method(f, fprime, R = 0, max_iter = 1000, tol=1e-3, args = [], debug = False):\n",
        "    count = 0\n",
        "    epsilon = 1\n",
        "    f_return = []\n",
        "    fprime_return = []\n",
        "\n",
        "    while epsilon >= tol:\n",
        "        count += 1\n",
        "        if count >= max_iter:\n",
        "            print('Sortie sur boucle infinie.')\n",
        "            return (R, count)\n",
        "\n",
        "        old_R = R\n",
        "\n",
        "        function_value = f(R, args = args)\n",
        "        function_derivative = fprime(R, args = args)\n",
        "        ind = np.where(function_derivative <= 0)\n",
        "        ind = ind[0]\n",
        "\n",
        "        R = -function_value / function_derivative + R\n",
        "\n",
        "        if ind.size > 0:\n",
        "            R[ ind ] = R[ ind ] * 0.5 + R[ ind ]\n",
        "\n",
        "        if np.isscalar(R):\n",
        "            epsilon = np.abs( (R - old_R) /old_R )\n",
        "        else:\n",
        "            epsilon = np.linalg.norm( R - old_R, np.Inf)\n",
        "\n",
        "        if debug == True:\n",
        "            f_return.append(function_value)\n",
        "            fprime_return.append(function_derivative)\n",
        "\n",
        "    return R, count, epsilon, function_value, function_derivative, f_return, fprime_return"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kZzkw8C9DHjX"
      },
      "source": [
        "Ce code définit une fonction newton_methode qui implémente la méthode de Newton pour la recherche de racines. Elle prend une fonction f et sa dérivée fprime, ainsi que d'autres paramètres optionnels, et retourne la racine trouvée après un certain nombre d'itérations. La méthode de Newton utilise des approximations linéaires pour trouver les zéros d'une fonction."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q61KSbo4Dt5o"
      },
      "source": [
        "Définissons notre fonction objectif pour le modèle Bachelier et calculons vega en utilisant la même technique de différenciation que celle utilisée ci-dessus."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "qXm8-qbT20FM"
      },
      "outputs": [],
      "source": [
        "def call_ba_objective_function(sigma, args):\n",
        "    S = args[0]\n",
        "    K = args[1]\n",
        "    r = args[2]\n",
        "    t = args[3]\n",
        "    price = args[4]\n",
        "\n",
        "    return bachelier(sigma, S, K, r, t) - price\n",
        "\n",
        "def calculate_vega_ba(sigma, args):\n",
        "    S = args[0]\n",
        "    K = args[1]\n",
        "    r = args[2]\n",
        "    t = args[3]\n",
        "\n",
        "    epsilon = 1e-6\n",
        "    C1 = bachelier(sigma, S, K, r, t)\n",
        "    C2 = bachelier(sigma + epsilon, S, K, r, t)\n",
        "\n",
        "    return (C2 - C1) / epsilon\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nfgJuwnX20FN"
      },
      "source": [
        "Nous verrons si nous pouvons reproduire la volatilité utilisée ci-dessus. Dans ce cas, le prix du call était en $"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "7031KGWj20FN"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_7798/490780487.py:17: DeprecationWarning: Calling nonzero on 0d arrays is deprecated, as it behaves surprisingly. Use `atleast_1d(cond).nonzero()` if the old behavior was intended. If the context of this warning is of the form `arr[nonzero(cond)]`, just use `arr[cond]`.\n",
            "  ind = np.where(function_derivative <= 0)\n"
          ]
        }
      ],
      "source": [
        "C0 = 3.6445730260768543\n",
        "S = 105\n",
        "K = 105\n",
        "r = 0.01\n",
        "t = 30/365\n",
        "\n",
        "args = (S, K, r, t, C0)\n",
        "\n",
        "R, count, epsilon, function_value, function_derivative, f_return, fprime_return = newtons_method(call_ba_objective_function, calculate_vega_ba, 0.5, args = args)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7BCErRZA20FN",
        "outputId": "b70728dd-7dc5-45a0-f671-8b7fb80b7443"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.3000000000000008\n"
          ]
        }
      ],
      "source": [
        "print(R / S)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EkLgIqsQ20FN"
      },
      "source": [
        "##  Prix ​​Bachelier d'un put\n",
        "\n",
        "Nous avons déjà une expression et codé une fonction pour le prix d'achat.  Nous pouvons utiliser la parité put-call pour trouver le prix d'une option put\n",
        "\n",
        "Une manière courante d'énoncer la parité put-call est,\n",
        "$$C - P = S - e^{-rt}K.$$\n",
        "\n",
        "Ainsi, si l’on connaît le prix d’un call, on peut obtenir le prix du put correspondant,\n",
        "$$P = C - S + e^{-rt}K.$$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "Vt-uc6mC20FO"
      },
      "outputs": [],
      "source": [
        "t = 30 / 365    # Délai jusqu'à l'expiration\n",
        "sigma = 0.30    # Volatilité implicite de Black Scholes\n",
        "K = 90          # Prix d'exercice\n",
        "r = 0.01        # Taux sans risque\n",
        "S = np.linspace(50, 110, 100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "id": "k1YNt4Y320FO",
        "outputId": "aaa5a1dd-d917-43c6-8aff-269c3322bcfe"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_7798/261312224.py:14: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k\" (-> color=(0.1, 0.1, 0.1, 1)). The keyword argument will take precedence.\n",
            "  plt.plot(S, P_bs, 'k', label = 'Black Scholes', color='red')\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, \"Prix d'achat (Call) ($)\")"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Calcul du prix de vente (put) de Black Schole\n",
        "P_bs = put_price(sigma, S, K, r, t)\n",
        "\n",
        "# Calcul du prix d'achat (call) de Bachelier\n",
        "\n",
        "C = bachelier(sigma * S, S, K, r, t)\n",
        "\n",
        "# Utilisons la parité put-call pour calculer le prix de vente\n",
        "\n",
        "P = C - S + np.exp(-r * t) * K\n",
        "\n",
        "\n",
        "#  Visualisons les résultats\n",
        "plt.plot(S, P_bs, 'k', label = 'Black Scholes', color='red')\n",
        "plt.plot(S, P, 'b.', label = 'Bachelier')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlabel(\"Prix ​​de l'action (4)\")\n",
        "plt.ylabel(\"Prix d'achat (Call) ($)\")"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.13"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}