EquityOption.cpp

### A free/open-source library for quantitative finance

EquityOption.cpp

This example evaluates European, American and Bermudan options using different methods.

    /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

    // the only header you need to use QuantLib
    #include <ql/quantlib.hpp>

    #ifdef BOOST_MSVC
    /* Uncomment the following lines to unmask floating-point
       exceptions. Warning: unpredictable results can arise...

       See http://www.wilmott.com/messageview.cfm?catid=10&threadid=9481
       Is there anyone with a definitive word about this?
    */
    // #include <float.h>
    // namespace { unsigned int u = _controlfp(_EM_INEXACT, _MCW_EM); }
    #endif

    #include <boost/timer.hpp>
    #include <iostream>
    #include <iomanip>

    using namespace QuantLib;

    #if defined(QL_ENABLE_SESSIONS)
    namespace QuantLib {

        Integer sessionId() { return 0; }

    }
    #endif

    int main(int, char* []) {

        try {

            boost::timer timer;
            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);

            boost::shared_ptr<Exercise> europeanExercise(
                                             new EuropeanExercise(maturity));

            boost::shared_ptr<Exercise> bermudanExercise(
                                             new BermudanExercise(exerciseDates));

            boost::shared_ptr<Exercise> americanExercise(
                                             new AmericanExercise(settlementDate,
                                                                  maturity));

            Handle<Quote> underlyingH(
                boost::shared_ptr<Quote>(new SimpleQuote(underlying)));

            // bootstrap the yield/dividend/vol curves
            Handle<YieldTermStructure> flatTermStructure(
                boost::shared_ptr<YieldTermStructure>(
                    new FlatForward(settlementDate, riskFreeRate, dayCounter)));
            Handle<YieldTermStructure> flatDividendTS(
                boost::shared_ptr<YieldTermStructure>(
                    new FlatForward(settlementDate, dividendYield, dayCounter)));
            Handle<BlackVolTermStructure> flatVolTS(
                boost::shared_ptr<BlackVolTermStructure>(
                    new BlackConstantVol(settlementDate, calendar, volatility,
                                         dayCounter)));
            boost::shared_ptr<StrikedTypePayoff> payoff(
                                            new PlainVanillaPayoff(type, strike));
            boost::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(boost::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;

            // semi-analytic Heston for European
            method = "Heston semi-analytic";
            boost::shared_ptr<HestonProcess> hestonProcess(
                new HestonProcess(flatTermStructure, flatDividendTS,
                                  underlyingH, volatility*volatility,
                                  1.0, volatility*volatility, 0.001, 0.0));
            boost::shared_ptr<HestonModel> hestonModel(
                                                  new HestonModel(hestonProcess));
            europeanOption.setPricingEngine(boost::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";
            boost::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));
            boost::shared_ptr<BatesModel> batesModel(new BatesModel(batesProcess));
            europeanOption.setPricingEngine(boost::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(boost::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(boost::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(boost::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";
            europeanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                     new FDEuropeanEngine<CrankNicolson>(bsmProcess,
                                                         timeSteps,timeSteps-1)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                     new FDBermudanEngine<CrankNicolson>(bsmProcess,
                                                         timeSteps,timeSteps-1)));
            americanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                     new FDAmericanEngine<CrankNicolson>(bsmProcess,
                                                         timeSteps,timeSteps-1)));
            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(boost::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps)));
            americanOption.setPricingEngine(boost::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(boost::shared_ptr<PricingEngine>(
                          new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess,
                                                                       timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                          new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess,
                                                                       timeSteps)));
            americanOption.setPricingEngine(boost::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(boost::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess,
                                                                       timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess,
                                                                       timeSteps)));
            americanOption.setPricingEngine(boost::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(boost::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                    new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps)));
            americanOption.setPricingEngine(boost::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(boost::shared_ptr<PricingEngine>(
                          new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                          new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps)));
            americanOption.setPricingEngine(boost::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(boost::shared_ptr<PricingEngine>(
                  new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                  new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps)));
            americanOption.setPricingEngine(boost::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(boost::shared_ptr<PricingEngine>(
                        new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps)));
            bermudanOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
                        new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps)));
            americanOption.setPricingEngine(boost::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;
            boost::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

            boost::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)";
            boost::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
            Real seconds = timer.elapsed();
            Integer hours = int(seconds/3600);
            seconds -= hours * 3600;
            Integer minutes = int(seconds/60);
            seconds -= minutes * 60;
            std::cout << " \nRun completed in ";
            if (hours > 0)
                std::cout << hours << " h ";
            if (hours > 0 || minutes > 0)
                std::cout << minutes << " m ";
            std::cout << std::fixed << std::setprecision(0)
                      << seconds << " s\n" << std::endl;
            return 0;

        } catch (std::exception& e) {
            std::cerr << e.what() << std::endl;
            return 1;
        } catch (...) {
            std::cerr << "unknown error" << std::endl;
            return 1;
        }
    }