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;

#ifdef BOOST_MSVC
#  ifdef QL_ENABLE_THREAD_SAFE_OBSERVER_PATTERN
#    include <ql/auto_link.hpp>
#    define BOOST_LIB_NAME boost_system
#    include <boost/config/auto_link.hpp>
#    undef BOOST_LIB_NAME
#    define BOOST_LIB_NAME boost_thread
#    include <boost/config/auto_link.hpp>
#    undef BOOST_LIB_NAME
#  endif
#endif


#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
        double 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;
    }
}