341 lines
8.1 KiB
Plaintext
341 lines
8.1 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "42505bbc",
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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": "880f1027",
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"metadata": {},
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"source": [
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"This code calculates the theta (time decay) of an American call option on Apple Inc. (AAPL) stock using QuantLib and OpenBB libraries. It fetches option chains and historical prices, determines the closest strike price, and computes volatility. The code then sets up the market data, constructs a Black-Scholes-Merton process, and uses a binomial pricing engine to price the option. Finally, it computes and returns the theta of the call option, which measures the sensitivity of the option's price to the passage of time."
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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": "b7d1894f",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import QuantLib as ql\n",
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"from openbb import obb\n",
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"import warnings"
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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": "5d7816ee",
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"metadata": {},
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"outputs": [],
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"source": [
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"warnings.filterwarnings(\"ignore\")\n",
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"obb.user.preferences.output_type = \"dataframe\""
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]
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},
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{
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"cell_type": "markdown",
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"id": "eb909667",
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"metadata": {},
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"source": [
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"Define the stock symbol and fetch option chains and historical prices"
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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": "f10f430b",
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"metadata": {},
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"outputs": [],
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"source": [
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"symbol = \"AAPL\"\n",
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"chains = obb.derivatives.options.chains(symbol=symbol)\n",
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"prices = obb.equity.price.historical(symbol=symbol, provider=\"yfinance\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5c8fec35",
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"metadata": {},
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"source": [
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"Select an expiration date and fetch associated strike prices"
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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": "dd6d5806",
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"metadata": {},
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"outputs": [],
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"source": [
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"expiration = chains.expiration.unique()[5]\n",
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"strikes = chains.query(\"`expiration` == @expiration\").strike.to_frame()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3647823f",
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"metadata": {},
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"source": [
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"Determine the underlying stock price and identify the closest strike price"
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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": "083edc0e",
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"metadata": {},
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"outputs": [],
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"source": [
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"underlying_price = prices.close.iat[-1]\n",
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"strike_price = (\n",
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" strikes\n",
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" .loc[\n",
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" (strikes-underlying_price)\n",
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" .abs()\n",
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" .sort_values(\"strike\")\n",
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" .index[0]\n",
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" ].strike\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": "0df0957c",
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"metadata": {},
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"source": [
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"Calculate volatility, maturity, dividend yield, and risk-free rate"
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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": "9c2877f3",
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"metadata": {},
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"outputs": [],
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"source": [
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"volatility = prices.close.pct_change().std() * np.sqrt(252)\n",
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"maturity = ql.Date(\n",
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" expiration.day,\n",
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" expiration.month,\n",
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" expiration.year,\n",
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")\n",
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"dividend_yield = 0.0056\n",
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"risk_free_rate = 0.05\n",
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"calculation_date = ql.Date.todaysDate()\n",
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"ql.Settings.instance().evaluationDate = calculation_date"
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]
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},
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{
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"cell_type": "markdown",
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"id": "450e1ab7",
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"metadata": {},
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"source": [
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"Set up the market data including spot price, yield term structure, dividend yield, and volatility"
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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": "0e239f26",
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"metadata": {},
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"outputs": [],
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"source": [
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"spot_handle = ql.QuoteHandle(\n",
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" ql.SimpleQuote(underlying_price)\n",
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")"
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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": "cc227df6",
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"metadata": {},
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"outputs": [],
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"source": [
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"yield_handle = ql.YieldTermStructureHandle(\n",
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" ql.FlatForward(\n",
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" calculation_date, \n",
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" risk_free_rate, \n",
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" ql.Actual365Fixed()\n",
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" )\n",
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")"
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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": "8a0ec3ad",
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"metadata": {},
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"outputs": [],
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"source": [
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"dividend_handle = ql.YieldTermStructureHandle(\n",
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" ql.FlatForward(\n",
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" calculation_date, \n",
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" dividend_yield, \n",
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" ql.Actual365Fixed()\n",
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" )\n",
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")"
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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": "b5a2786d",
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"metadata": {},
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"outputs": [],
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"source": [
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"volatility_handle = ql.BlackVolTermStructureHandle(\n",
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" ql.BlackConstantVol(\n",
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" calculation_date, \n",
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" ql.NullCalendar(), \n",
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" volatility, \n",
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" ql.Actual365Fixed()\n",
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" )\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": "c3e37c12",
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"metadata": {},
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"source": [
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"Construct a Black-Scholes-Merton process for option pricing"
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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": "793fa60b",
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"metadata": {},
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"outputs": [],
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"source": [
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"bs_process = ql.BlackScholesMertonProcess(\n",
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" spot_handle, \n",
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" dividend_handle, \n",
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" yield_handle, \n",
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" volatility_handle\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": "f33a6256",
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"metadata": {},
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"source": [
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"Set up the pricing engine using a binomial tree model with 1000 steps"
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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": "ba4f9584",
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"metadata": {},
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"outputs": [],
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"source": [
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"engine = ql.BinomialVanillaEngine(bs_process, \"crr\", steps=1000)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cdf6482d",
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"metadata": {},
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"source": [
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"Define the American call option with the calculated strike price and maturity"
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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": "70cd1554",
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"metadata": {},
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"outputs": [],
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"source": [
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"exercise = ql.AmericanExercise(calculation_date, maturity) \n",
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"call_option = ql.VanillaOption(\n",
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" ql.PlainVanillaPayoff(ql.Option.Call, strike_price),\n",
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" exercise\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": "f383f8e7",
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"metadata": {},
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"source": [
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"Assign the pricing engine to the 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": "321c90a8",
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"metadata": {},
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"outputs": [],
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"source": [
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"call_option.setPricingEngine(engine)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ff91901c",
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"metadata": {},
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"source": [
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"Calculate and return the theta of the call option, normalized by the number of days in a year"
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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": "7770ed99",
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"metadata": {},
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"outputs": [],
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"source": [
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"call_theta = call_option.theta() / 365\n",
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"call_theta"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fb0a8d41",
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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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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.13"
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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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