Modèles_de_Bachelier_et_Black_Scholes_en_Python.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "view-in-github"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Evilafo/Finance/blob/main/Mod%C3%A8les_de_Bachelier_et_Black_Scholes_en_Python.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "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_7035/1240337607.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": 11,
      "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": 12,
      "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": 13,
      "metadata": {
        "id": "7031KGWj20FN"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_7035/490780487.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": 14,
      "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",
        "$$P = C - S + e^{-rt}K.$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "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": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "id": "k1YNt4Y320FO",
        "outputId": "aaa5a1dd-d917-43c6-8aff-269c3322bcfe"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "<ipython-input-72-218bd3fd48c8>: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) ($)\")"
            ]
          },
          "execution_count": 72,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Calcul du prix de vente (put) de Black Schole\n",
        "P_bs = put_price(sigma, S, K, r, t)\n",
        "\n",
        "# Calcul du prix d'achat (call) de Bachelier\n",
        "\n",
        "C = bachelier(sigma * S, S, K, r, t)\n",
        "\n",
        "# Utilisons la parité put-call pour calculer le prix de vente\n",
        "\n",
        "P = C - S + np.exp(-r * t) * K\n",
        "\n",
        "\n",
        "#  Visualisons les résultats\n",
        "plt.plot(S, P_bs, 'k', label = 'Black Scholes', color='red')\n",
        "plt.plot(S, P, 'b.', label = 'Bachelier')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlabel(\"Prix ​​de l'action (4)\")\n",
        "plt.ylabel(\"Prix d'achat (Call) ($)\")"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "include_colab_link": true,
      "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
}