478 lines
11 KiB
Plaintext
478 lines
11 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "fa226836",
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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": "71f198b7",
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"metadata": {},
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"source": [
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"This code calculates the implied and realized volatility of an asset, and evaluates the payoff of a volatility swap. It uses QuantLib to set up financial instruments and yield curves, and NumPy and Pandas for simulations and calculations. First, it calculates the implied volatility from the market price of a European option using the Black-Scholes model. Then, it simulates asset price paths to compute realized volatility. Finally, it calculates the value of a volatility swap based on these volatilities."
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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": "aebedeea",
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"metadata": {},
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"outputs": [],
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"source": [
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"import QuantLib as ql\n",
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"import numpy as np\n",
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"import pandas as pd"
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]
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},
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{
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"cell_type": "markdown",
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"id": "afba19b8",
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"metadata": {},
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"source": [
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"Define financial parameters such as notional amount, volatility strike, days to maturity, and observation period"
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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": "8babe8d0",
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"metadata": {},
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"outputs": [],
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"source": [
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"notional = 100_000 \n",
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"volatility_strike = 0.2438\n",
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"days_to_maturity = 148\n",
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"observation_period = 252"
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]
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},
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{
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"cell_type": "markdown",
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"id": "095d1289",
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"metadata": {},
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"source": [
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"Define additional financial parameters such as risk-free rate, dividend yield, and current spot 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": "0465a508",
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"metadata": {},
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"outputs": [],
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"source": [
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"risk_free_rate = 0.0525\n",
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"dividend_yield = 0.0052\n",
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"spot_price = 188.64"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5b2c2242",
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"metadata": {},
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"source": [
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"Create calendar and day count convention objects for use in QuantLib calculations"
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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": "184f9cea",
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"metadata": {},
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"outputs": [],
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"source": [
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"calendar = ql.NullCalendar()\n",
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"day_count = ql.Actual360()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c5ab97e8",
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"metadata": {},
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"source": [
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"Set today's date and evaluation date in QuantLib"
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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": "9340a5d8",
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"metadata": {},
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"outputs": [],
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"source": [
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"today = ql.Date().todaysDate()\n",
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"ql.Settings.instance().evaluationDate = today"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ed0a8506",
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"metadata": {},
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"source": [
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"Create the risk-free rate term structure handle using a flat forward curve"
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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": "176f2878",
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"metadata": {},
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"outputs": [],
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"source": [
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"risk_free_ts = ql.YieldTermStructureHandle(\n",
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" ql.FlatForward(today, risk_free_rate, day_count)\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": "5f2dfc50",
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"metadata": {},
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"source": [
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"Create the dividend yield term structure handle using a flat forward curve"
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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": "ad960a14",
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"metadata": {},
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"outputs": [],
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"source": [
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"dividend_ts = ql.YieldTermStructureHandle(\n",
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" ql.FlatForward(today, dividend_yield, day_count)\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": "e3f40a4f",
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"metadata": {},
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"source": [
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"Create the spot price handle using a simple quote"
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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": "d1e4912d",
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"metadata": {},
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"outputs": [],
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"source": [
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"spot_handle = ql.QuoteHandle(ql.SimpleQuote(spot_price))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "62fea0f2",
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"metadata": {},
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"source": [
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"Define parameters for the European option including strike price, market price, and expiration date"
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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": "2f5df3be",
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"metadata": {},
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"outputs": [],
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"source": [
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"strike_price = 190\n",
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"option_price = 11.05\n",
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"expiration_date = today + ql.Period(days_to_maturity, ql.Days)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "19846fe1",
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"metadata": {},
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"source": [
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"Set up the option with a plain vanilla payoff and European exercise"
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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": "74083fa4",
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"metadata": {},
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"outputs": [],
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"source": [
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"payoff = ql.PlainVanillaPayoff(ql.Option.Call, strike_price)\n",
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"exercise = ql.EuropeanExercise(expiration_date)\n",
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"european_option = ql.VanillaOption(payoff, exercise)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9c2377f9",
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"metadata": {},
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"source": [
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"Set up the volatility structure with an initial guess for implied 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": "da3828fd",
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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(today, calendar, volatility_strike, day_count)\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": "cfe48958",
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"metadata": {},
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"source": [
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"Use the 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": "d5cb1639",
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"metadata": {},
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"outputs": [],
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"source": [
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"bsm_process = ql.BlackScholesMertonProcess(\n",
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" spot_handle, dividend_ts, risk_free_ts, 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": "3e912452",
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"metadata": {},
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"source": [
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"Calculate the implied volatility from the market price of the 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": "7bf19f08",
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"metadata": {},
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"outputs": [],
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"source": [
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"implied_volatility = european_option.impliedVolatility(\n",
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" option_price, bsm_process, 1e-4, 1000, 1e-8, 4.0\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": "30681256",
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"metadata": {},
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"outputs": [],
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"source": [
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"print(f\"Implied Volatility: {implied_volatility:.4f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2f3ce2ad",
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"metadata": {},
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"source": [
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"Set the random seed for reproducibility and define simulation 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": "c65b7472",
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"metadata": {},
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"outputs": [],
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"source": [
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"np.random.seed(42)\n",
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"time_steps = observation_period\n",
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"dt = 1 / observation_period"
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]
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},
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{
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"cell_type": "markdown",
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"id": "99f00915",
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"metadata": {},
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"source": [
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"Initialize an array to store simulated asset prices and set the initial 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": "c1d53659",
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"metadata": {},
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"outputs": [],
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"source": [
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"prices = np.zeros((time_steps + 1, 1))\n",
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"prices[0] = spot_price"
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]
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},
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{
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"cell_type": "markdown",
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"id": "47b026f4",
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"metadata": {},
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"source": [
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"Simulate asset price paths using a geometric Brownian motion 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": "6a86ebdc",
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"metadata": {},
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"outputs": [],
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"source": [
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"for t in range(1, time_steps + 1):\n",
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" z = np.random.normal(size=1)\n",
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" prices[t] = (\n",
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" prices[t-1] \n",
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" * np.exp(\n",
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" (risk_free_rate - 0.5 * implied_volatility**2) * \n",
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" dt + \n",
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" implied_volatility * \n",
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" np.sqrt(dt) * z\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": "0129e267",
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"metadata": {},
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"source": [
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"Convert the simulated prices to a pandas DataFrame for further analysis"
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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": "a96eb0e0",
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"metadata": {},
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"outputs": [],
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"source": [
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"prices_df = pd.DataFrame(prices, columns=['Price'])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fa7e51f8",
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"metadata": {},
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"source": [
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"Calculate daily returns from the simulated 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": "721ae250",
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"metadata": {},
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"outputs": [],
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"source": [
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"prices_df['Return'] = prices_df['Price'].pct_change().dropna()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "89a06767",
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"metadata": {},
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"source": [
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"Calculate realized volatility from the daily returns"
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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": "92d2be43",
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"metadata": {},
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"outputs": [],
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"source": [
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"realized_volatility = np.std(prices_df['Return']) * np.sqrt(observation_period)"
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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": "8190344a",
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"metadata": {},
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"outputs": [],
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"source": [
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"print(f\"Realized Volatility: {realized_volatility:.4f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bccc2823",
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"metadata": {},
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"source": [
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"Calculate the time to maturity in years"
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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": "06aa9217",
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"metadata": {},
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"outputs": [],
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"source": [
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"time_to_maturity = days_to_maturity / observation_period"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c5dd73ce",
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"metadata": {},
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"source": [
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"Calculate the payoff of the volatility swap based on realized and strike 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": "830e946c",
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"metadata": {},
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"outputs": [],
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"source": [
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"volatility_swap_value = (\n",
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" (realized_volatility - volatility_strike) * \n",
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" notional * \n",
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" np.sqrt(time_to_maturity)\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": "15e99f26",
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"metadata": {},
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"outputs": [],
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"source": [
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"print(f\"Volatility Swap Value: ${volatility_swap_value:.2f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2ad683ab",
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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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