{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Stochastic modelling and derivatives in traditional markets and in crypto-markets - TD 2 - Corrigé" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice 1: Pricing d'options européennes dans le modèle binomial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On s'intéresse au calcul du prix d'un payoff Européen $\\Psi(S_{t_n})$ dans le modèle binomial avec paramètres $ u> d$, valeur initial de l'actif $S_0$, et en présence d'un taux d'intéret $r$ sur chaque période: $1$ Euro en $t_i$ devient $1+r$ Euros en $t_{i+1}$.\n", "\n", "#### $\\blacktriangleright$ Portefeuille de couverture\n", "\n", "Comme démontré dans le cours, en supposant un modèle binomial, pour chaque payoff $\\Psi(S_{t_n})$ il existe un unique portefeuille autofinançant $(V_{t_i})_{i=0,\\dots,n}$ qui réplique exactement le payoff à maturité. \n", "\n", "Ce portefeuille s'écrit à chaque date $t_i$ comme une fonction $v(t_i, S_{t_i})$ de la valeur courante du sous-jacent en $t_i$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Questions 1 et 2: nous répondons ci-dessous aux deux questions simultanément, en utilisant la meme fonction pour calculer le prix $V_{t_i} = v(t_i, S_{t_i})$ et le delta $\\delta(t_i, S_{t_i})$ de l'option à chaque date $t_i$ ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tout d'abord, nous définissons une fonction Python qui renvoie la fonction valeur du portefeuille $v(t_i, \\cdot)$ à la date $t_i$ et son delta $\\delta(t_i, \\cdot)$ à partir de la connaissance de la fonction valeur $v(t_{i+1}, \\cdot)$ à la date $t_{i+1}$ suivante." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def recursion(r, u, d, fonction_prix_t_i_plus_one, delta_flag=0):\n", " \"\"\"\n", " On effectue une itération de la date t_{i+1} à la date t_i.\n", " \n", " Paramètres\n", " + r, u, d: les paramètres du modèle binomial \n", " + fonction_prix_t_i_plus_one (une fonction Python):\n", " La fonction de prix v(t_{i+1}, .) à la date t_{i+1}.\n", " Doit prendre comme argument la valeur S_{t_{i+1}} du sous-jacent à la date t_{i+1}.\n", " \n", " Output:\n", " + Une fonction Python, la fonction de prix v(t_i, .) à la date t_i.\n", " Doit prendre comme argument la valeur S_{t_i} du sous-jacent.\n", " \n", " + Si delta_flag: renvoie une autre fonction Python, le delta delta(t_i, .) du portefeuille à la date t_i.\n", " Doit prendre comme argument la valeur S_{t_i} du sous-jacent.\n", " \"\"\"\n", " q_up = (1 + r - d) / (u - d)\n", " q_down = 1 - q_up\n", " \n", " def fonction_prix_t_i(S):\n", " valeur = (fonction_prix_t_i_plus_one(S*u)*q_up + fonction_prix_t_i_plus_one(S*d)*q_down) / (1+r)\n", " return valeur\n", " \n", " if delta_flag:\n", " def delta_t_i(S):\n", " delta = (fonction_prix_t_i_plus_one(S*u) - fonction_prix_t_i_plus_one(S*d)) / (S*(u - d))\n", " return delta\n", " \n", " if delta_flag == 0:\n", " return fonction_prix_t_i\n", " \n", " else:\n", " return fonction_prix_t_i, delta_t_i" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons déjà tester, pour le problème à $n=1$ période, le pricing d'un call $\\Psi(S) = (S-K)^+$ (considéré dans le cours)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "S_0 = 4\n", "u_u = 2\n", "d = 1/2\n", "r = 1/4\n", "K = 5\n", "\n", "## On verifie la condition d'absence d'arbitrage sur le marché contenant S et le taux r:\n", "assert(d < 1 + r < u_u)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculons le prix en $t_0 = 0$ de l'option $\\Psi(S_{t_1})$, et son delta:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Prix en t_0 du call de payoff (S_{t_1} - 5.0)^+: 1.20\n", "Delta en t_0 du call de payoff (S_{t_1} - 5.0)^+: 0.50\n" ] } ], "source": [ "def payoff_call(S, strike = K):\n", " return np.maximum(S - strike, 0)\n", "\n", "fonction_prix, fonction_delta = recursion(r, u_u, d, payoff_call, delta_flag=1)\n", "\n", "prix = fonction_prix(S_0)\n", "delta = fonction_delta(S_0)\n", "\n", "print(\"Prix en t_0 du call de payoff (S_{t_1} - %1.1f)^+: %1.2f\" %(K, prix))\n", "\n", "print(\"Delta en t_0 du call de payoff (S_{t_1} - %1.1f)^+: %1.2f\" %(K, delta))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cas à $n$ dates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans le cas $n$ dates $t_1, \\dots, t_n$, on peut procéder de manière rétrograde pour calculer le prix et le delta en $t_0$ (et à toute date $t_i$, en fait) d'un payoff $\\Psi(S_{t_n})$.\n", "\n", "On pourra donc faire appel à la fonction prix_recursion (en appliquant le nombre approprié d'itérations)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def recursion_n_i(r, u, d, payoff, i, n, delta_flag=0):\n", " \"\"\"\n", " On effectue les itérations de la date t_n à à la date t_i, i < n,\n", " pour l'option de maturité t_n et de payoff = payoff(S_{t_n})\n", " \n", " Output: une fonction Python, la fonction de prix v(t_i, .) à la date t_i.\n", " Cette fonction prendra comme argument la valeur S_{t_i} du sous-jacent.\n", " \n", " Output:\n", " + Une fonction Python, la fonction de prix v(t_i, .) à la date t_i.\n", " \n", " + Si delta_flag: on renvoie la fonction de prix v(t_i, .) ET le delta(t_i, .)\n", " du portefeuille de couverture à la date t_i.\n", " Ces fonctions prendront comme argument la valeur S_{t_i} du sous-jacent.\n", " \n", " \"\"\"\n", " fonction_prix_et_delta = [payoff, 0]\n", " \n", " for j in range(n, i, -1):\n", " fonction_prix_et_delta = recursion(r, u, d, fonction_prix_et_delta[0], delta_flag=1)\n", " ## la variable fonction_prix_et_delta contient un couple de fonctions\n", " \n", " if delta_flag == 0:\n", " return fonction_prix_et_delta[0]\n", " \n", " else:\n", " return fonction_prix_et_delta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Toujours pour le payoff $\\Psi(S) = (S-K)^+$ défini plus haut, on peut maintenant calculer le prix et le delta à n'importe quelle date $t_i$ pour une maturité $t_n > t_i$:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Prix en t_0 du call de payoff (S_{t_13} - 99.22)^+ lorsque S_{t_0} = 99.120: 9.195\n", "Delta en t_0 du call de payoff (S_{t_13} - 99.22)^+ lorsque S_{t_0} = 99.120: 0.616\n" ] } ], "source": [ "n = 13\n", "i = 0\n", "S_ti = 99.12; u = 1.0514; d = (1.0-0.0489); r = 0.0031; K = 99.22\n", "\n", "assert(d < 1 + r < u)\n", "\n", "def payoff_call(S, strike = K):\n", " return np.maximum(S- strike, 0)\n", "\n", "fonction_prix, fonction_delta = recursion_n_i(r, u, d, payoff_call, i, n, delta_flag=1)\n", "\n", "prix = fonction_prix(S_ti)\n", "delta = fonction_delta(S_ti)\n", "\n", "print(\"Prix en t_%1.0f du call de payoff (S_{t_%1.0f} - %1.2f)^+ lorsque S_{t_%1.0f} = %1.3f: %1.3f\" %(i, n, K, i, S_ti, prix))\n", "\n", "print(\"Delta en t_%1.0f du call de payoff (S_{t_%1.0f} - %1.2f)^+ lorsque S_{t_%1.0f} = %1.3f: %1.3f\" %(i, n, K, i, S_ti, delta))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Prix en t_0 du put de payoff (S_{t_8} - 100.40)^+ lorsque S_{t_0} = 100.360: 16.694\n", "Delta en t_0 du put de payoff (S_{t_8} - 100.40)^+ lorsque S_{t_0} = 100.360: 0.644\n" ] } ], "source": [ "n = 8\n", "i = 0\n", "\n", "S_ti = 100.36; u = 1.1335; d = 1.0/1.1178; r = 0.0088; K = 100.40\n", "\n", "assert(d < 1 + r < u)\n", "\n", "def payoff_call(S, strike = K):\n", " return np.maximum(S - K, 0)\n", "\n", "fonction_prix, fonction_delta = recursion_n_i(r, u, d, payoff_call, i, n, delta_flag=1)\n", "\n", "prix = fonction_prix(S_ti)\n", "delta = fonction_delta(S_ti)\n", "\n", "print(\"Prix en t_%1.0f du put de payoff (S_{t_%1.0f} - %1.2f)^+ lorsque S_{t_%1.0f} = %1.3f: %1.3f\" %(i, n, K, i, S_ti, prix))\n", "\n", "print(\"Delta en t_%1.0f du put de payoff (S_{t_%1.0f} - %1.2f)^+ lorsque S_{t_%1.0f} = %1.3f: %1.3f\" %(i, n, K, i, S_ti, delta))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Vérifier que le prix comptant du payoff $S_{t_n}$ dans ce modèle est bien égal à $S_0$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Prix en t_0 de S_{t_8} lorsque S_0 vaut 4.00: 4.00\n" ] } ], "source": [ "i = 0\n", "\n", "def payoff_forward(S):\n", " return S\n", "\n", "fonction_prix = recursion_n_i(r, u, d, payoff_forward, i, n)\n", "prix = fonction_prix(S_0)\n", "\n", "print(\"Prix en t_%1.0f de S_{t_%1.0f} lorsque S_0 vaut %1.2f: %1.2f\" %(i, n, S_0, prix))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 Afficher la fonction de prix $v(t_0, S_0)$ d'un call $(S_{t_n} - K)^+$ de strike et maturité donnés en fonction de la valeur de $S_0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons également afficher le delta de l'option: nous allons calculer prix et delta sur la meme grille de valeur du spot $S_0$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "## Une grille de 50 valeurs du sous-jacent S_0 entre K/3 et 2*K\n", "nb_points = 50\n", "spots = np.linspace(K/3, 2*K, nb_points)\n", "\n", "call_prices = np.zeros(nb_points)\n", "deltas = np.zeros(nb_points)\n", "\n", "n = 10\n", "i = 0\n", "\n", "## Le payoff du call de strike K = 120 a été défini plus haut \n", "fonction_prix, fonction_delta = recursion_n_i(r, u, d, payoff_call, i, n, delta_flag=1)\n", "\n", "for j, S in enumerate(spots): \n", " call_prices[j] = fonction_prix(S)\n", " deltas[j] = fonction_delta(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons maintenant afficher les prix calculés en fonction de la valeur du spot $S_0$, ainsi que la borne inférieure pour un prix de call (valide dans n'importe quel modèle):\n", "$$\n", "C( (S_{t_n} - K)^+, t_n) \\ge C( S_{t_n} - K, t_n) = S_{t_0} - K B(t_0, t_n)\n", "= S_{t_0} - \\frac{K}{(1+r)^{t_n}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.figure()\n", "## On affiche les prix en fonction des valeurs du spot\n", "plt.plot(spots, call_prices, color=\"b\", label=\"Call price\")\n", "\n", "## On affiche la borne inf en fonction du spot\n", "borne_inf = np.maximum(spots - K/(1+r)**n, 0) \n", "\n", "plt.plot(spots, borne_inf, color=\"k\", label=u\"Borne inf $(S - K/(1+r)^n)^+$\")\n", "\n", "plt.xlabel(\"spot S\", fontsize=12)\n", "plt.ylabel(\"price\", fontsize=12)\n", "\n", "plt.legend(loc=\"best\", fontsize=12)\n", "\n", "###################################################################\n", "## Dans une autre figure, on affiche le delta en fonction du spot\n", "###################################################################\n", "plt.figure()\n", "\n", "plt.plot(spots, deltas, color=\"g\", label=\"Delta du call\")\n", "plt.axhline(1.0, color=\"k\")\n", "\n", "plt.xlabel(\"spot S\", fontsize=12)\n", "plt.ylabel(\"delta\", fontsize=12)\n", "\n", "plt.legend(loc=\"best\", fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3 Alternativement, calculer les prix du call $(S_{t_n} - K)^+$ pour différents prix d'exercice $K$ (et une meme maturité $t_n$) et afficher les prix en fonction de leur strike." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "## Une grille de 50 strikes entre S_0/3 et 3*S_0\n", "nb_points = 50\n", "strikes = np.linspace(S_0/3, 3*S_0, nb_points)\n", "\n", "call_prices = np.zeros(nb_points)\n", "\n", "## On calcule les prix en t_0 = 0 des calls correspondants\n", "n = 10\n", "i = 0\n", "\n", "for j, K in enumerate(strikes):\n", " \n", " def payoff_call(S):\n", " return np.maximum(S - K, 0)\n", "\n", " fonction_prix = recursion_n_i(r, u, d, payoff_call, i, n)\n", "\n", " call_prices[j] = fonction_prix(S_0)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "## On affiche les prix en fonction des strikes\n", "plt.plot(strikes, call_prices, color=\"b\", label=\"Call price\")\n", "\n", "## On affiche la borne inf en fonction des strikes\n", "borne_inf = np.maximum(S_0 - strikes/(1+r)**n, 0) \n", "\n", "plt.plot(strikes, borne_inf, color=\"k\", label=u\"Borne inf $(S_0 - K/(1+r)^n)^+$\")\n", "\n", "plt.xlabel(\"strike K\", fontsize=12)\n", "plt.ylabel(\"price\", fontsize=12)\n", "\n", "plt.legend(loc=\"best\", fontsize=12)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.13.5" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": false, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }