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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*!
Copyright (C) 2005, 2006, 2007, 2009 StatPro Italia srl
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.
*/
#include <ql/qldefines.hpp>
#if !defined(BOOST_ALL_NO_LIB) && defined(BOOST_MSVC)
# include <ql/auto_link.hpp>
#endif
#include <ql/instruments/vanillaoption.hpp>
#include <ql/math/integrals/tanhsinhintegral.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanvasicekengine.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
#include <ql/pricingengines/vanilla/baroneadesiwhaleyengine.hpp>
#include <ql/pricingengines/vanilla/batesengine.hpp>
#include <ql/pricingengines/vanilla/binomialengine.hpp>
#include <ql/pricingengines/vanilla/bjerksundstenslandengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/pricingengines/vanilla/integralengine.hpp>
#include <ql/pricingengines/vanilla/mcamericanengine.hpp>
#include <ql/pricingengines/vanilla/mceuropeanengine.hpp>
#include <ql/pricingengines/vanilla/qdfpamericanengine.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <iostream>
#include <iomanip>
using namespace QuantLib;
int main(int, char* []) {
try {
std::cout << std::endl;
// set up dates
Calendar calendar = TARGET();
Date todaysDate(15, May, 1998);
Date settlementDate(17, May, 1998);
Settings::instance().evaluationDate() = todaysDate;
// our options
Option::Type type(Option::Put);
Real underlying = 36;
Real strike = 40;
Spread dividendYield = 0.00;
Rate riskFreeRate = 0.06;
Volatility volatility = 0.20;
Date maturity(17, May, 1999);
DayCounter dayCounter = Actual365Fixed();
std::cout << "Option type = " << type << std::endl;
std::cout << "Maturity = " << maturity << std::endl;
std::cout << "Underlying price = " << underlying << std::endl;
std::cout << "Strike = " << strike << std::endl;
std::cout << "Risk-free interest rate = " << io::rate(riskFreeRate)
<< std::endl;
std::cout << "Dividend yield = " << io::rate(dividendYield)
<< std::endl;
std::cout << "Volatility = " << io::volatility(volatility)
<< std::endl;
std::cout << std::endl;
std::string method;
std::cout << std::endl ;
// write column headings
Size widths[] = { 35, 14, 14, 14 };
std::cout << std::setw(widths[0]) << std::left << "Method"
<< std::setw(widths[1]) << std::left << "European"
<< std::setw(widths[2]) << std::left << "Bermudan"
<< std::setw(widths[3]) << std::left << "American"
<< std::endl;
std::vector<Date> exerciseDates;
for (Integer i=1; i<=4; i++)
exerciseDates.push_back(settlementDate + 3*i*Months);
auto europeanExercise = ext::make_shared<EuropeanExercise>(maturity);
auto bermudanExercise = ext::make_shared<BermudanExercise>(exerciseDates);
auto americanExercise = ext::make_shared<AmericanExercise>(settlementDate, maturity);
auto underlyingH = makeQuoteHandle(underlying);
// bootstrap the yield/dividend/vol curves
Handle<YieldTermStructure> flatTermStructure(
ext::make_shared<FlatForward>(settlementDate, riskFreeRate, dayCounter));
Handle<YieldTermStructure> flatDividendTS(
ext::make_shared<FlatForward>(settlementDate, dividendYield, dayCounter));
Handle<BlackVolTermStructure> flatVolTS(
ext::make_shared<BlackConstantVol>(settlementDate, calendar, volatility,
dayCounter));
auto payoff = ext::make_shared<PlainVanillaPayoff>(type, strike);
auto bsmProcess = ext::make_shared<BlackScholesMertonProcess>(
underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
// options
VanillaOption europeanOption(payoff, europeanExercise);
VanillaOption bermudanOption(payoff, bermudanExercise);
VanillaOption americanOption(payoff, americanExercise);
// Analytic formulas:
// Black-Scholes for European
method = "Black-Scholes";
europeanOption.setPricingEngine(ext::make_shared<AnalyticEuropeanEngine>(bsmProcess));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
//Vasicek rates model for European
method = "Black Vasicek Model";
Real r0 = riskFreeRate;
Real a = 0.3;
Real b = 0.3;
Real sigma_r = 0.15;
Real riskPremium = 0.0;
Real correlation = 0.5;
auto vasicekProcess = ext::make_shared<Vasicek>(r0, a, b, sigma_r, riskPremium);
europeanOption.setPricingEngine(ext::make_shared<AnalyticBlackVasicekEngine>(bsmProcess, vasicekProcess, correlation));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// semi-analytic Heston for European
method = "Heston semi-analytic";
auto hestonProcess = ext::make_shared<HestonProcess>(flatTermStructure, flatDividendTS,
underlyingH, volatility*volatility,
1.0, volatility*volatility, 0.001, 0.0);
auto hestonModel = ext::make_shared<HestonModel>(hestonProcess);
europeanOption.setPricingEngine(ext::make_shared<AnalyticHestonEngine>(hestonModel));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// semi-analytic Bates for European
method = "Bates semi-analytic";
auto batesProcess = ext::make_shared<BatesProcess>(flatTermStructure, flatDividendTS,
underlyingH, volatility*volatility,
1.0, volatility*volatility, 0.001, 0.0,
1e-14, 1e-14, 1e-14);
auto batesModel = ext::make_shared<BatesModel>(batesProcess);
europeanOption.setPricingEngine(ext::make_shared<BatesEngine>(batesModel));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Barone-Adesi and Whaley approximation for American
method = "Barone-Adesi/Whaley";
americanOption.setPricingEngine(ext::make_shared<BaroneAdesiWhaleyApproximationEngine>(bsmProcess));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Bjerksund and Stensland approximation for American
method = "Bjerksund/Stensland";
americanOption.setPricingEngine(ext::make_shared<BjerksundStenslandApproximationEngine>(bsmProcess));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// QD+ fixed-point engine for American
method = "QD+ fixed-point (fast)";
americanOption.setPricingEngine(ext::make_shared<QdFpAmericanEngine>
(bsmProcess, QdFpAmericanEngine::fastScheme()));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
method = "QD+ fixed-point (accurate)";
americanOption.setPricingEngine(ext::make_shared<QdFpAmericanEngine>
(bsmProcess, QdFpAmericanEngine::accurateScheme()));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
method = "QD+ fixed-point (high precision)";
americanOption.setPricingEngine(ext::make_shared<QdFpAmericanEngine>
(bsmProcess, QdFpAmericanEngine::highPrecisionScheme()));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Integral
method = "Integral";
europeanOption.setPricingEngine(ext::make_shared<IntegralEngine>(bsmProcess));
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Finite differences
Size timeSteps = 801;
method = "Finite differences";
auto fdengine =
ext::make_shared<FdBlackScholesVanillaEngine>(bsmProcess,
timeSteps,
timeSteps-1);
europeanOption.setPricingEngine(fdengine);
bermudanOption.setPricingEngine(fdengine);
americanOption.setPricingEngine(fdengine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Jarrow-Rudd
method = "Binomial Jarrow-Rudd";
auto jrEngine = ext::make_shared<BinomialVanillaEngine<JarrowRudd>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(jrEngine);
bermudanOption.setPricingEngine(jrEngine);
americanOption.setPricingEngine(jrEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Cox-Ross-Rubinstein
method = "Binomial Cox-Ross-Rubinstein";
auto crrEngine = ext::make_shared<BinomialVanillaEngine<CoxRossRubinstein>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(crrEngine);
bermudanOption.setPricingEngine(crrEngine);
americanOption.setPricingEngine(crrEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Additive equiprobabilities
method = "Additive equiprobabilities";
auto aeqpEngine = ext::make_shared<BinomialVanillaEngine<AdditiveEQPBinomialTree>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(aeqpEngine);
bermudanOption.setPricingEngine(aeqpEngine);
americanOption.setPricingEngine(aeqpEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Trigeorgis
method = "Binomial Trigeorgis";
auto trigeorgisEngine = ext::make_shared<BinomialVanillaEngine<Trigeorgis>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(trigeorgisEngine);
bermudanOption.setPricingEngine(trigeorgisEngine);
americanOption.setPricingEngine(trigeorgisEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Tian
method = "Binomial Tian";
auto tianEngine = ext::make_shared<BinomialVanillaEngine<Tian>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(tianEngine);
bermudanOption.setPricingEngine(tianEngine);
americanOption.setPricingEngine(tianEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Leisen-Reimer
method = "Binomial Leisen-Reimer";
auto lrEngine = ext::make_shared<BinomialVanillaEngine<LeisenReimer>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(lrEngine);
bermudanOption.setPricingEngine(lrEngine);
americanOption.setPricingEngine(lrEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Binomial method: Binomial Joshi
method = "Binomial Joshi";
auto joshiEngine = ext::make_shared<BinomialVanillaEngine<Joshi4>>(bsmProcess, timeSteps);
europeanOption.setPricingEngine(joshiEngine);
bermudanOption.setPricingEngine(joshiEngine);
americanOption.setPricingEngine(joshiEngine);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << bermudanOption.NPV()
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// Monte Carlo Method: MC (crude)
timeSteps = 1;
method = "MC (crude)";
Size mcSeed = 42;
auto mcengine1 = MakeMCEuropeanEngine<PseudoRandom>(bsmProcess)
.withSteps(timeSteps)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed);
europeanOption.setPricingEngine(mcengine1);
// Real errorEstimate = europeanOption.errorEstimate();
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Monte Carlo Method: QMC (Sobol)
method = "QMC (Sobol)";
Size nSamples = 32768; // 2^15
auto mcengine2 = MakeMCEuropeanEngine<LowDiscrepancy>(bsmProcess)
.withSteps(timeSteps)
.withSamples(nSamples);
europeanOption.setPricingEngine(mcengine2);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << europeanOption.NPV()
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << "N/A"
<< std::endl;
// Monte Carlo Method: MC (Longstaff Schwartz)
method = "MC (Longstaff Schwartz)";
auto mcengine3 = MakeMCAmericanEngine<PseudoRandom>(bsmProcess)
.withSteps(100)
.withAntitheticVariate()
.withCalibrationSamples(4096)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed);
americanOption.setPricingEngine(mcengine3);
std::cout << std::setw(widths[0]) << std::left << method
<< std::fixed
<< std::setw(widths[1]) << std::left << "N/A"
<< std::setw(widths[2]) << std::left << "N/A"
<< std::setw(widths[3]) << std::left << americanOption.NPV()
<< std::endl;
// End test
return 0;
} catch (std::exception& e) {
std::cerr << e.what() << std::endl;
return 1;
} catch (...) {
std::cerr << "unknown error" << std::endl;
return 1;
}
}
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