EquityOption.cpp

For a given set of option parameters, this example computes the value of three different equity options types (with european, bermudan and american exercise features) using different valuation algorithms. The calculation methods are Black-Scholes (for european options only), Barone-Adesi/Whaley (american-only), Bjerksund/Stensland (american), Integral (european), finite differences, binomial trees, crude Monte Carlo (european-only) and Sobol-sequence Monte Carlo (european-only).

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
#include <ql/qldefines.hpp>
#ifdef BOOST_MSVC
#  include <ql/auto_link.hpp>
#endif
#include <ql/instruments/vanillaoption.hpp>
#include <ql/pricingengines/vanilla/binomialengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
#include <ql/pricingengines/vanilla/baroneadesiwhaleyengine.hpp>
#include <ql/pricingengines/vanilla/bjerksundstenslandengine.hpp>
#include <ql/pricingengines/vanilla/batesengine.hpp>
#include <ql/pricingengines/vanilla/integralengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/pricingengines/vanilla/mceuropeanengine.hpp>
#include <ql/pricingengines/vanilla/mcamericanengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanvasicekengine.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/models/shortrate/onefactormodels/vasicek.hpp>
 
#include <iostream>
#include <iomanip>
 
using namespace QuantLib;
 
#if defined(QL_ENABLE_SESSIONS)
namespace QuantLib {
 
    ThreadKey sessionId() { return 0; }
 
}
#endif
 
 
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);
 
        ext::shared_ptr<Exercise> europeanExercise(
                                         new EuropeanExercise(maturity));
 
        ext::shared_ptr<Exercise> bermudanExercise(
                                         new BermudanExercise(exerciseDates));
 
        ext::shared_ptr<Exercise> americanExercise(
                                         new AmericanExercise(settlementDate,
                                                              maturity));
 
        Handle<Quote> underlyingH(
            ext::shared_ptr<Quote>(new SimpleQuote(underlying)));
 
        // bootstrap the yield/dividend/vol curves
        Handle<YieldTermStructure> flatTermStructure(
            ext::shared_ptr<YieldTermStructure>(
                new FlatForward(settlementDate, riskFreeRate, dayCounter)));
        Handle<YieldTermStructure> flatDividendTS(
            ext::shared_ptr<YieldTermStructure>(
                new FlatForward(settlementDate, dividendYield, dayCounter)));
        Handle<BlackVolTermStructure> flatVolTS(
            ext::shared_ptr<BlackVolTermStructure>(
                new BlackConstantVol(settlementDate, calendar, volatility,
                                     dayCounter)));
        ext::shared_ptr<StrikedTypePayoff> payoff(
                                        new PlainVanillaPayoff(type, strike));
        ext::shared_ptr<BlackScholesMertonProcess> bsmProcess(
                 new 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::shared_ptr<PricingEngine>(
                                     new 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;
        ext::shared_ptr<Vasicek> vasicekProcess(new Vasicek(r0, a, b, sigma_r, riskPremium));
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new 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";
        ext::shared_ptr<HestonProcess> hestonProcess(
            new HestonProcess(flatTermStructure, flatDividendTS,
                              underlyingH, volatility*volatility,
                              1.0, volatility*volatility, 0.001, 0.0));
        ext::shared_ptr<HestonModel> hestonModel(
                                              new HestonModel(hestonProcess));
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                                     new 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";
        ext::shared_ptr<BatesProcess> batesProcess(
            new BatesProcess(flatTermStructure, flatDividendTS,
                             underlyingH, volatility*volatility,
                             1.0, volatility*volatility, 0.001, 0.0,
                             1e-14, 1e-14, 1e-14));
        ext::shared_ptr<BatesModel> batesModel(new BatesModel(batesProcess));
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                                                new 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::shared_ptr<PricingEngine>(
                       new 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::shared_ptr<PricingEngine>(
                      new 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;
 
        // Integral
        method = "Integral";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                                             new 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";
        ext::shared_ptr<PricingEngine> 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";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps)));
        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;
        method = "Binomial Cox-Ross-Rubinstein";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess,
                                                                   timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess,
                                                                   timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess,
                                                                   timeSteps)));
        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";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess,
                                                                   timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess,
                                                                   timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess,
                                                                   timeSteps)));
        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";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps)));
        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";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps)));
        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";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
              new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
              new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
              new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps)));
        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";
        europeanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps)));
        bermudanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps)));
        americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps)));
        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;
        ext::shared_ptr<PricingEngine> mcengine1;
        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
 
        ext::shared_ptr<PricingEngine> mcengine2;
        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)";
        ext::shared_ptr<PricingEngine> mcengine3;
        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;
    }
}