daily update
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David Brazda
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to_explore/pyquantnews/38_AmericanOptionPricer.ipynb
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190
to_explore/pyquantnews/38_AmericanOptionPricer.ipynb
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "9d21a51c",
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"metadata": {},
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"source": [
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"<div style=\"background-color:#000;\"><img src=\"pqn.png\"></img></div>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "658dd5ee",
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"metadata": {},
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"source": [
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"This code implements a binomial model to price American options, considering early exercise features. Using parameters like spot price, strike price, risk-free rate, volatility, time to expiry, and the number of steps, the model constructs a price tree. It then calculates the option value at each node, considering both holding and exercising the option. This approach is practical for valuing American-style options, which can be exercised at any time before expiration."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8791fb6f",
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"metadata": {
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"lines_to_next_cell": 1
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},
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"outputs": [],
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"source": [
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"import numpy as np"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9af5deeb",
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"metadata": {},
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"source": [
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"Define a function to price American options using the binomial tree model"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f00b850d",
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"metadata": {
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"lines_to_next_cell": 1
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},
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"outputs": [],
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"source": [
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"def american_option_pricer(spot, strike, rate, vol, expiry, steps, option_type):\n",
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" \"\"\"Price an American option using binomial model\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" spot : float\n",
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" Current spot price of the underlying asset\n",
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" strike : float\n",
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" Strike price of the option\n",
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" rate : float\n",
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" Risk-free interest rate\n",
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" vol : float\n",
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" Volatility of the underlying asset\n",
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" expiry : float\n",
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" Time to expiry in years\n",
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" steps : int\n",
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" Number of steps in the binomial tree\n",
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" option_type : str\n",
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" Type of the option ('call' or 'put')\n",
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" \n",
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" Returns\n",
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" -------\n",
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" float\n",
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" Estimated price of the American option\n",
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" \n",
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" Notes\n",
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" -----\n",
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" This function constructs a binomial tree to \n",
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" estimate the price of an American option. It \n",
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" accounts for early exercise features by comparing \n",
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" the value of holding versus exercising the option \n",
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" at each node.\n",
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" \"\"\"\n",
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"\n",
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" # Calculate the time interval and the up and down factors\n",
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"\n",
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" dt = expiry / steps\n",
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" u = np.exp(vol * np.sqrt(dt))\n",
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" d = 1 / u\n",
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"\n",
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" # Calculate the risk-neutral probability\n",
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"\n",
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" p = (np.exp(rate * dt) - d) / (u - d)\n",
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"\n",
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" # Create the binomial price tree\n",
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"\n",
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" price_tree = np.zeros((steps + 1, steps + 1))\n",
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" for i in range(steps + 1):\n",
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" price_tree[i, -1] = spot * (u ** (steps - i)) * (d**i)\n",
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"\n",
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" # Calculate the option value at each node\n",
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"\n",
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" option_tree = np.zeros_like(price_tree)\n",
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" if option_type.lower() == \"call\":\n",
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" option_tree[:, -1] = np.maximum(price_tree[:, -1] - strike, 0)\n",
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" elif option_type.lower() == \"put\":\n",
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" option_tree[:, -1] = np.maximum(strike - price_tree[:, -1], 0)\n",
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" else:\n",
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" raise ValueError(\"Option type must be either 'call' or 'put'.\")\n",
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"\n",
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" # Traverse the tree backward to find the option price today\n",
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"\n",
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" for t in range(steps - 1, -1, -1):\n",
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" for i in range(t + 1):\n",
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" exercise = 0\n",
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" if option_type.lower() == \"call\":\n",
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" exercise = price_tree[i, t] - strike\n",
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" elif option_type.lower() == \"put\":\n",
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" exercise = strike - price_tree[i, t]\n",
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"\n",
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" hold = np.exp(-rate * dt) * (\n",
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" p * option_tree[i, t + 1] + (1 - p) * option_tree[i + 1, t + 1]\n",
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" )\n",
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" option_tree[i, t] = np.maximum(exercise, hold)\n",
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"\n",
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" return option_tree[0, 0]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cba2ebed",
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"metadata": {},
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"source": [
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"Estimate the price of an American Call option using the defined binomial model parameters"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e615d29c",
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"metadata": {},
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"outputs": [],
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"source": [
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"option_price = american_option_pricer(\n",
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" spot=55.0,\n",
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" strike=50.0,\n",
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" rate=0.05,\n",
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" vol=0.3,\n",
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" expiry=1.0,\n",
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" steps=100,\n",
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" option_type=\"Call\",\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a87537d8",
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"metadata": {},
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"source": [
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"Print the estimated price of the American Call option"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5118d3b2",
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"metadata": {},
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"outputs": [],
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"source": [
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"print(\n",
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" f\"The estimated price of the American Call option is: {option_price:.2f}\"\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "16e10849",
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"metadata": {},
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"source": [
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"<a href=\"https://pyquantnews.com/\">PyQuant News</a> is where finance practitioners level up with Python for quant finance, algorithmic trading, and market data analysis. Looking to get started? Check out the fastest growing, top-selling course to <a href=\"https://gettingstartedwithpythonforquantfinance.com/\">get started with Python for quant finance</a>. For educational purposes. Not investment advise. Use at your own risk."
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "-all"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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