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/*
Copyright (C) 2007 Eric H. Jensen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
using System;
using System.Collections.Generic;
using System.Text;
using QuantLib;
namespace EquityOptionTest
{
class EquityOption
{
/// <summary>
/// The main entry point for the application.
/// </summary>
[STAThread]
static void Main(string[] args)
{
DateTime startTime = DateTime.Now;
Option.Type optionType = Option.Type.Put;
double underlyingPrice = 36;
double strikePrice = 40;
double dividendYield = 0.0;
double riskFreeRate = 0.06;
double volatility = 0.2;
Date todaysDate = new Date(15, Month.May, 1998);
Settings.instance().setEvaluationDate(todaysDate);
Date settlementDate = new Date(17, Month.May, 1998);
Date maturityDate = new Date(17, Month.May, 1999);
Calendar calendar = new TARGET();
DateVector exerciseDates = new DateVector(4);
for (int i = 1; i <= 4; i++) {
Period forwardPeriod = new Period(3 * i, TimeUnit.Months);
Date forwardDate = settlementDate.Add(forwardPeriod);
exerciseDates.Add(forwardDate);
}
EuropeanExercise europeanExercise =
new EuropeanExercise(maturityDate);
BermudanExercise bermudanExercise =
new BermudanExercise(exerciseDates);
AmericanExercise americanExercise =
new AmericanExercise(settlementDate, maturityDate);
// bootstrap the yield/dividend/vol curves and create a
// BlackScholesMerton stochastic process
DayCounter dayCounter = new Actual365Fixed();
YieldTermStructureHandle flatRateTSH =
new YieldTermStructureHandle(
new FlatForward(settlementDate, riskFreeRate,
dayCounter));
YieldTermStructureHandle flatDividendTSH =
new YieldTermStructureHandle(
new FlatForward(settlementDate, dividendYield,
dayCounter));
BlackVolTermStructureHandle flatVolTSH =
new BlackVolTermStructureHandle(
new BlackConstantVol(settlementDate, calendar,
volatility, dayCounter));
QuoteHandle underlyingQuoteH =
new QuoteHandle(new SimpleQuote(underlyingPrice));
BlackScholesMertonProcess stochasticProcess =
new BlackScholesMertonProcess(underlyingQuoteH,
flatDividendTSH,
flatRateTSH,
flatVolTSH);
PlainVanillaPayoff payoff =
new PlainVanillaPayoff(optionType, strikePrice);
// options
VanillaOption europeanOption =
new VanillaOption(payoff, europeanExercise);
VanillaOption bermudanOption =
new VanillaOption(payoff, bermudanExercise);
VanillaOption americanOption =
new VanillaOption(payoff, americanExercise);
// report the parameters we are using
ReportParameters(optionType, underlyingPrice, strikePrice,
dividendYield, riskFreeRate,
volatility, maturityDate);
// write out the column headings
ReportHeadings();
#region Analytic Formulas
// Black-Scholes for European
try {
europeanOption.setPricingEngine(
new AnalyticEuropeanEngine(stochasticProcess));
ReportResults("Black-Scholes",
europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Barone-Adesi and Whaley approximation for American
try {
americanOption.setPricingEngine(
new BaroneAdesiWhaleyEngine(stochasticProcess));
ReportResults("Barone-Adesi/Whaley",
null, null, americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Bjerksund and Stensland approximation for American
try {
americanOption.setPricingEngine(
new BjerksundStenslandEngine(stochasticProcess));
ReportResults("Bjerksund/Stensland",
null, null, americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Integral
try {
europeanOption.setPricingEngine(
new IntegralEngine(stochasticProcess));
ReportResults("Integral",
europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
uint timeSteps = 801;
// Finite differences
try {
europeanOption.setPricingEngine(
new FDEuropeanEngine(stochasticProcess,
timeSteps, timeSteps - 1));
bermudanOption.setPricingEngine(
new FDBermudanEngine(stochasticProcess,
timeSteps, timeSteps - 1));
americanOption.setPricingEngine(
new FDAmericanEngine(stochasticProcess,
timeSteps, timeSteps - 1));
ReportResults("Finite differences",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
#endregion Analytic Formulas
#region Binomial Methods
// Binomial Jarrow-Rudd
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"jarrowrudd", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"jarrowrudd", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"jarrowrudd", timeSteps));
ReportResults("Binomial Jarrow-Rudd",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Cox-Ross-Rubinstein
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"coxrossrubinstein", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"coxrossrubinstein", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"coxrossrubinstein", timeSteps));
ReportResults("Binomial Cox-Ross-Rubinstein",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Additive Equiprobabilities
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"eqp", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"eqp", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"eqp", timeSteps));
ReportResults("Additive Equiprobabilities",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Trigeorgis
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"trigeorgis", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"trigeorgis", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"trigeorgis", timeSteps));
ReportResults("Binomial Trigeorgis",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Tian
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"tian", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"tian", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"tian", timeSteps));
ReportResults("Binomial Tian",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Leisen-Reimer
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"leisenreimer", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"leisenreimer", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"leisenreimer", timeSteps));
ReportResults("Binomial Leisen-Reimer",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Joshi
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"joshi4", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"joshi4", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"joshi4", timeSteps));
ReportResults("Binomial Joshi",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
#endregion Binomial Methods
#region Monte Carlo Methods
// quantlib appears to use max numeric (int and real) values to test for 'null' (or rather 'default') values
// MC (crude)
try {
string traits = "pseudorandom";
int mcTimeSteps = 1;
int timeStepsPerYear = int.MaxValue;
bool brownianBridge = false;
bool antitheticVariate = false;
bool controlVariate = false;
int requiredSamples = int.MaxValue;
double requiredTolerance = 0.02;
int maxSamples = int.MaxValue;
int seed = 42;
europeanOption.setPricingEngine(
new MCEuropeanEngine(stochasticProcess,
traits, mcTimeSteps,
timeStepsPerYear,
brownianBridge,
antitheticVariate,
controlVariate,
requiredSamples,
requiredTolerance,
maxSamples, seed));
ReportResults("MC (crude)", europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// MC (Sobol)
try {
string traits = "lowdiscrepancy";
int mcTimeSteps = 1;
int timeStepsPerYear = int.MaxValue;
bool brownianBridge = false;
bool antitheticVariate = false;
bool controlVariate = false;
int requiredSamples = 32768; // 2^15
double requiredTolerance = double.MaxValue;
int maxSamples = int.MaxValue;
int seed = 0;
europeanOption.setPricingEngine(
new MCEuropeanEngine(stochasticProcess,
traits, mcTimeSteps,
timeStepsPerYear,
brownianBridge,
antitheticVariate,
controlVariate,
requiredSamples,
requiredTolerance, maxSamples, seed));
ReportResults("MC (Sobol)", europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// MC (Longstaff Schwartz)
/*
try {
// MCAmericanEngine is not currently exposed in SWIG
//americanOption.setPricingEngine(new MCAmericanEngine());
ReportResults("MC (Longstaff Schwartz)", null, null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
*/
#endregion Monte Carlo Methods
DateTime endTime = DateTime.Now;
TimeSpan delta = endTime - startTime;
Console.WriteLine();
Console.WriteLine("Run completed in {0} s", delta.TotalSeconds);
Console.WriteLine();
}
private static void ReportParameters(Option.Type optionType,
double underlyingPrice,
double strikePrice,
double dividendYield,
double riskFreeRate,
double volatility,
Date maturityDate)
{
Console.WriteLine();
Console.WriteLine("Option type = {0}", optionType);
Console.WriteLine("Maturity = {0} {1} {2}", maturityDate.year(),
maturityDate.month(), maturityDate.dayOfMonth());
Console.WriteLine("Underlying price = ${0}", underlyingPrice);
Console.WriteLine("Strike = ${0}", strikePrice);
Console.WriteLine("Risk-free interest rate = {0}%",
riskFreeRate * 100.0);
Console.WriteLine("Dividend yield = {0}%", dividendYield * 100.0);
Console.WriteLine("Volatility = {0}%", volatility * 100);
Console.WriteLine();
}
private static int[] columnWidths = { 35, 14, 14, 14 };
private static void ReportHeadings()
{
Console.Write("Method".PadRight(columnWidths[0]));
Console.Write("European".PadRight(columnWidths[1]));
Console.Write("Bermudan".PadRight(columnWidths[2]));
Console.Write("American".PadRight(columnWidths[3]));
Console.WriteLine();
}
private static void ReportResults(string methodName, double? european,
double? bermudan, double? american)
{
string strNA = "N/A";
string format = "{0:N6}";
Console.Write(methodName.PadRight(columnWidths[0]));
Console.Write(String.Format((european == null) ? strNA : format,
european).PadRight(columnWidths[1]));
Console.Write(String.Format((bermudan == null) ? strNA : format,
bermudan).PadRight(columnWidths[2]));
Console.Write(String.Format((american == null) ? strNA : format,
american).PadRight(columnWidths[3]));
Console.WriteLine();
}
}
}
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