C++：实现量化Forward option远期合约期权测试实例

#include "forwardoption.hpp"
#include "utilities.hpp"
#include <ql/time/daycounters/actual360.hpp>
#include <ql/instruments/forwardvanillaoption.hpp>
#include <ql/models/equity/hestonmodel.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
#include <ql/pricingengines/vanilla/binomialengine.hpp>
#include <ql/pricingengines/forward/forwardengine.hpp>
#include <ql/pricingengines/forward/forwardperformanceengine.hpp>
#include <ql/pricingengines/forward/mcforwardeuropeanbsengine.hpp>
#include <ql/pricingengines/forward/mcforwardeuropeanhestonengine.hpp>
#include <ql/experimental/forward/analytichestonforwardeuropeanengine.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/processes/hestonprocess.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <map>using namespace QuantLib;
using namespace boost::unit_test_framework;#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoff, exercise, s, q, r, today, \v, moneyness, reset, expected, calculated, \error, tolerance) \BOOST_ERROR("Forward " << exerciseTypeToString(exercise) << " " \<< payoff->optionType() << " option with " \<< payoffTypeToString(payoff) << " payoff:\n" \<< "    spot value:        " << s << "\n" \<< "    strike:            " << payoff->strike() <<"\n" \<< "    moneyness:         " << moneyness << "\n" \<< "    dividend yield:    " << io::rate(q) << "\n" \<< "    risk-free rate:    " << io::rate(r) << "\n" \<< "    reference date:    " << today << "\n" \<< "    reset date:        " << reset << "\n" \<< "    maturity:          " << exercise->lastDate() << "\n" \<< "    volatility:        " << io::volatility(v) << "\n\n" \<< "    expected   " << greekName << ": " << expected << "\n" \<< "    calculated " << greekName << ": " << calculated << "\n"\<< "    error:            " << error << "\n" \<< "    tolerance:        " << tolerance);namespace {struct ForwardOptionData {Option::Type type;Real moneyness;Real s;          // spotRate q;          // dividendRate r;          // risk-free rateTime start;      // time to resetTime t;          // time to maturityVolatility v;    // volatilityReal result;     // expected resultReal tol;        // tolerance};}void ForwardOptionTest::testValues() {BOOST_TEST_MESSAGE("Testing forward option values...");/* The data below are from"Option pricing formulas", E.G. Haug, McGraw-Hill 1998*/ForwardOptionData values[] = {//  type, moneyness, spot,  div, rate,start,   t,  vol, result, tol// "Option pricing formulas", pag. 37{ Option::Call, 1.1, 60.0, 0.04, 0.08, 0.25, 1.0, 0.30, 4.4064, 1.0e-4 },// "Option pricing formulas", VBA code{  Option::Put, 1.1, 60.0, 0.04, 0.08, 0.25, 1.0, 0.30, 8.2971, 1.0e-4 }};DayCounter dc = Actual360();Date today = Settings::instance().evaluationDate();ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));Handle<YieldTermStructure> qTS(flatRate(today, qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));Handle<YieldTermStructure> rTS(flatRate(today, rRate, dc));ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));Handle<BlackVolTermStructure> volTS(flatVol(today, vol, dc));ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new BlackScholesMertonProcess(Handle<Quote>(spot),Handle<YieldTermStructure>(qTS),Handle<YieldTermStructure>(rTS),Handle<BlackVolTermStructure>(volTS)));ext::shared_ptr<PricingEngine> engine(new ForwardVanillaEngine<AnalyticEuropeanEngine>(stochProcess));for (auto& value : values) {ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(value.type, 0.0));Date exDate = today + timeToDays(value.t);ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + timeToDays(value.start);spot->setValue(value.s);qRate->setValue(value.q);rRate->setValue(value.r);vol->setValue(value.v);ForwardVanillaOption option(value.moneyness, reset, payoff, exercise);option.setPricingEngine(engine);Real calculated = option.NPV();Real error = std::fabs(calculated - value.result);Real tolerance = 1e-4;if (error>tolerance) {REPORT_FAILURE("value", payoff, exercise, value.s, value.q, value.r, today, value.v,value.moneyness, reset, value.result, calculated, error, tolerance);}}
}void ForwardOptionTest::testPerformanceValues() {BOOST_TEST_MESSAGE("Testing forward performance option values...");/* The data below are the performance equivalent of theforward options tested above and taken from"Option pricing formulas", E.G. Haug, McGraw-Hill 1998*/ForwardOptionData values[] = {//  type, moneyness, spot,  div, rate,start, maturity,  vol,                       result, tol{ Option::Call, 1.1, 60.0, 0.04, 0.08, 0.25,      1.0, 0.30, 4.4064/60*std::exp(-0.04*0.25), 1.0e-4 },{  Option::Put, 1.1, 60.0, 0.04, 0.08, 0.25,      1.0, 0.30, 8.2971/60*std::exp(-0.04*0.25), 1.0e-4 }};DayCounter dc = Actual360();Date today = Settings::instance().evaluationDate();ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));Handle<YieldTermStructure> qTS(flatRate(today, qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));Handle<YieldTermStructure> rTS(flatRate(today, rRate, dc));ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));Handle<BlackVolTermStructure> volTS(flatVol(today, vol, dc));ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new BlackScholesMertonProcess(Handle<Quote>(spot),Handle<YieldTermStructure>(qTS),Handle<YieldTermStructure>(rTS),Handle<BlackVolTermStructure>(volTS)));ext::shared_ptr<PricingEngine> engine(new ForwardPerformanceVanillaEngine<AnalyticEuropeanEngine>(stochProcess));for (auto& value : values) {ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(value.type, 0.0));Date exDate = today + timeToDays(value.t);ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + timeToDays(value.start);spot->setValue(value.s);qRate->setValue(value.q);rRate->setValue(value.r);vol->setValue(value.v);ForwardVanillaOption option(value.moneyness, reset, payoff, exercise);option.setPricingEngine(engine);Real calculated = option.NPV();Real error = std::fabs(calculated - value.result);Real tolerance = 1e-4;if (error>tolerance) {REPORT_FAILURE("value", payoff, exercise, value.s, value.q, value.r, today, value.v,value.moneyness, reset, value.result, calculated, error, tolerance);}}
}namespace {template <template <class> class Engine>void testForwardGreeks() {std::map<std::string,Real> calculated, expected, tolerance;tolerance["delta"]   = 1.0e-5;tolerance["gamma"]   = 1.0e-5;tolerance["theta"]   = 1.0e-5;tolerance["rho"]     = 1.0e-5;tolerance["divRho"]  = 1.0e-5;tolerance["vega"]    = 1.0e-5;Option::Type types[] = { Option::Call, Option::Put };Real moneyness[] = { 0.9, 1.0, 1.1 };Real underlyings[] = { 100.0 };Rate qRates[] = { 0.04, 0.05, 0.06 };Rate rRates[] = { 0.01, 0.05, 0.15 };Integer lengths[] = { 1, 2 };Integer startMonths[] = { 6, 9 };Volatility vols[] = { 0.11, 0.50, 1.20 };DayCounter dc = Actual360();Date today = Settings::instance().evaluationDate();ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));Handle<YieldTermStructure> qTS(flatRate(qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));Handle<YieldTermStructure> rTS(flatRate(rRate, dc));ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));ext::shared_ptr<PricingEngine> engine(new Engine<AnalyticEuropeanEngine>(stochProcess));for (auto& type : types) {for (Real& moneynes : moneyness) {for (int length : lengths) {for (int startMonth : startMonths) {Date exDate = today + length * Years;ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + startMonth * Months;ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, 0.0));ForwardVanillaOption option(moneynes, reset, payoff, exercise);option.setPricingEngine(engine);for (Real u : underlyings) {for (Real m : qRates) {for (Real n : rRates) {for (Real v : vols) {Rate q = m, r = n;spot->setValue(u);qRate->setValue(q);rRate->setValue(r);vol->setValue(v);Real value = option.NPV();calculated["delta"] = option.delta();calculated["gamma"] = option.gamma();calculated["theta"] = option.theta();calculated["rho"] = option.rho();calculated["divRho"] = option.dividendRho();calculated["vega"] = option.vega();if (value > spot->value() * 1.0e-5) {// perturb spot and get delta and gammaReal du = u * 1.0e-4;spot->setValue(u + du);Real value_p = option.NPV(), delta_p = option.delta();spot->setValue(u - du);Real value_m = option.NPV(), delta_m = option.delta();spot->setValue(u);expected["delta"] = (value_p - value_m) / (2 * du);expected["gamma"] = (delta_p - delta_m) / (2 * du);// perturb rates and get rho and dividend rhoSpread dr = r * 1.0e-4;rRate->setValue(r + dr);value_p = option.NPV();rRate->setValue(r - dr);value_m = option.NPV();rRate->setValue(r);expected["rho"] = (value_p - value_m) / (2 * dr);Spread dq = q * 1.0e-4;qRate->setValue(q + dq);value_p = option.NPV();qRate->setValue(q - dq);value_m = option.NPV();qRate->setValue(q);expected["divRho"] = (value_p - value_m) / (2 * dq);// perturb volatility and get vegaVolatility dv = v * 1.0e-4;vol->setValue(v + dv);value_p = option.NPV();vol->setValue(v - dv);value_m = option.NPV();vol->setValue(v);expected["vega"] = (value_p - value_m) / (2 * dv);// perturb date and get thetaTime dT = dc.yearFraction(today - 1, today + 1);Settings::instance().evaluationDate() = today - 1;value_m = option.NPV();Settings::instance().evaluationDate() = today + 1;value_p = option.NPV();Settings::instance().evaluationDate() = today;expected["theta"] = (value_p - value_m) / dT;// comparestd::map<std::string, Real>::iterator it;for (it = calculated.begin(); it != calculated.end();++it) {std::string greek = it->first;Real expct = expected[greek],calcl = calculated[greek],tol = tolerance[greek];Real error = relativeError(expct, calcl, u);if (error > tol) {REPORT_FAILURE(greek, payoff, exercise, u, q, r,today, v, moneynes, reset, expct,calcl, error, tol);}}}}}}}}}}}}}void ForwardOptionTest::testGreeks() {BOOST_TEST_MESSAGE("Testing forward option greeks...");SavedSettings backup;testForwardGreeks<ForwardVanillaEngine>();
}void ForwardOptionTest::testPerformanceGreeks() {BOOST_TEST_MESSAGE("Testing forward performance option greeks...");SavedSettings backup;testForwardGreeks<ForwardPerformanceVanillaEngine>();
}class TestBinomialEngine : public BinomialVanillaEngine<CoxRossRubinstein>
{private:
public:explicit TestBinomialEngine(const ext::shared_ptr<GeneralizedBlackScholesProcess > &process): BinomialVanillaEngine<CoxRossRubinstein>(process, 300) // fixed steps{}
};void ForwardOptionTest::testGreeksInitialization() {BOOST_TEST_MESSAGE("Testing forward option greeks initialization...");DayCounter dc = Actual360();SavedSettings backup;Date today = Settings::instance().evaluationDate();ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(100.0));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.04));Handle<YieldTermStructure> qTS(flatRate(qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.01));Handle<YieldTermStructure> rTS(flatRate(rRate, dc));ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.11));Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));ext::shared_ptr<PricingEngine> engine(new ForwardVanillaEngine<TestBinomialEngine>(stochProcess));Date exDate = today + 1*Years;ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + 6*Months;ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(Option::Call, 0.0));ForwardVanillaOption option(0.9, reset, payoff, exercise);option.setPricingEngine(engine);ext::shared_ptr<PricingEngine> ctrlengine(new TestBinomialEngine(stochProcess));VanillaOption ctrloption(payoff, exercise);ctrloption.setPricingEngine(ctrlengine);Real delta = 0;try{delta = ctrloption.delta();}catch (const QuantLib::Error &) {// if normal option can't calculate delta,// nor should forwardtry{delta   = option.delta();}catch (const QuantLib::Error &) {delta = Null<Real>();}QL_REQUIRE(delta == Null<Real>(), "Forward delta invalid");}Real rho  = 0;try{rho = ctrloption.rho();}catch (const QuantLib::Error &) {// if normal option can't calculate rho,// nor should forwardtry{rho = option.rho();}catch (const QuantLib::Error &) {rho = Null<Real>();}QL_REQUIRE(rho == Null<Real>(), "Forward rho invalid");}Real divRho = 0;try{divRho = ctrloption.dividendRho();}catch (const QuantLib::Error &) {// if normal option can't calculate divRho,// nor should forwardtry{divRho = option.dividendRho();}catch (const QuantLib::Error &) {divRho = Null<Real>();}QL_REQUIRE(divRho == Null<Real>(), "Forward dividendRho invalid");}Real vega = 0;try{vega = ctrloption.vega();}catch (const QuantLib::Error &) {// if normal option can't calculate vega,// nor should forwardtry{vega = option.vega();}catch (const QuantLib::Error &) {vega = Null<Real>();}QL_REQUIRE(vega == Null<Real>(), "Forward vega invalid");}
}void ForwardOptionTest::testMCPrices() {BOOST_TEST_MESSAGE("Testing forward option MC prices...");Real tol[] = {0.002, 0.001, 0.0006, 5e-4, 5e-4};Size timeSteps = 100;Size numberOfSamples = 5000;Size mcSeed = 42;Real q = 0.04;Real r = 0.01;Real sigma = 0.11;Real s = 100;DayCounter dc = Actual360();SavedSettings backup;Date today = Settings::instance().evaluationDate();ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(s));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(q));Handle<YieldTermStructure> qTS(flatRate(qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(r));Handle<YieldTermStructure> rTS(flatRate(rRate, dc));ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(sigma));Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));ext::shared_ptr<PricingEngine> analyticEngine(new ForwardVanillaEngine<AnalyticEuropeanEngine>(stochProcess));ext::shared_ptr<PricingEngine> mcEngine = MakeMCForwardEuropeanBSEngine<PseudoRandom>(stochProcess).withSteps(timeSteps).withSamples(numberOfSamples).withSeed(mcSeed);Date exDate = today + 1*Years;ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + 6*Months;ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(Option::Call, 0.0));Real moneyness[] = { 0.8, 0.9, 1.0, 1.1, 1.2 };for (Size moneyness_index = 0; moneyness_index < LENGTH(moneyness); ++moneyness_index) {ForwardVanillaOption option(moneyness[moneyness_index], reset, payoff, exercise);option.setPricingEngine(analyticEngine);Real analyticPrice = option.NPV();option.setPricingEngine(mcEngine);Real mcPrice = option.NPV();Real error = relativeError(analyticPrice, mcPrice, s);if (error > tol[moneyness_index]) {REPORT_FAILURE("testMCPrices", payoff, exercise, s, q, r, today, sigma, moneyness[moneyness_index], reset,analyticPrice, mcPrice, error, tol[moneyness_index]);}}
}void ForwardOptionTest::testHestonMCPrices() {BOOST_TEST_MESSAGE("Testing forward option Heston MC prices...");Option::Type optionTypes[] = { Option::Call, Option::Put };Real mcForwardStartTolerance[][6] = {{7e-4,    // Call, moneyness=0.88e-4,    // Call, moneyness=0.96e-4,    // Call, moneyness=1.05e-4,    // Call, moneyness=1.15e-4},   // Call, moneyness=1.2{6e-4,    // Put, moneyness=0.85e-4,    // Put, moneyness=0.96e-4,    // Put, moneyness=1.00.001,   // Put, moneyness=1.10.001}}; // Put, moneyness=1.2Real tol[][6] = {{9e-4,    // Call, moneyness=0.89e-4,    // Call, moneyness=0.96e-4,    // Call, moneyness=1.05e-4,    // Call, moneyness=1.15e-4},   // Call, moneyness=1.2{6e-4,    // Put, moneyness=0.85e-4,    // Put, moneyness=0.98e-4,    // Put, moneyness=1.00.002,   // Put, moneyness=1.10.002}}; // Put, moneyness=1.2for (Size type_index = 0; type_index < LENGTH(optionTypes); ++type_index) {Real analyticTolerance = 5e-4;Size timeSteps = 50;Size numberOfSamples = 4095;Size mcSeed = 42;Real q = 0.04;Real r = 0.01;Real sigma_bs = 0.245;Real s = 100;// Test 1: Set up an equivalent flat Heston and compare to analytical BS pricingReal v0 = sigma_bs * sigma_bs;Real kappa = 1e-8;Real theta = sigma_bs * sigma_bs;Real sigma = 1e-8;Real rho = -0.93;DayCounter dc = Actual360();SavedSettings backup;Date today = Settings::instance().evaluationDate();Date exDate = today + 1 * Years;ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + 6 * Months;ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(optionTypes[type_index], 0.0));ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(s));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(q));Handle<YieldTermStructure> qTS(flatRate(qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(r));Handle<YieldTermStructure> rTS(flatRate(rRate, dc));ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(sigma_bs));Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));ext::shared_ptr<BlackScholesMertonProcess> bsProcess(new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));ext::shared_ptr<PricingEngine> analyticEngine(new ForwardVanillaEngine<AnalyticEuropeanEngine>(bsProcess));ext::shared_ptr<HestonProcess> hestonProcess(new HestonProcess(rTS, qTS, Handle<Quote>(spot), v0, kappa, theta, sigma, rho));ext::shared_ptr<PricingEngine> mcEngine =MakeMCForwardEuropeanHestonEngine<LowDiscrepancy>(hestonProcess).withSteps(timeSteps).withSamples(numberOfSamples).withSeed(mcSeed);Real moneyness[] = {0.8, 0.9, 1.0, 1.1, 1.2};for (Size moneyness_index = 0; moneyness_index < LENGTH(moneyness); ++moneyness_index) {ForwardVanillaOption option(moneyness[moneyness_index], reset, payoff, exercise);option.setPricingEngine(analyticEngine);Real analyticPrice = option.NPV();option.setPricingEngine(mcEngine);Real mcPrice = option.NPV();Real mcError = relativeError(analyticPrice, mcPrice, s);if (mcError > mcForwardStartTolerance[type_index][moneyness_index]) {REPORT_FAILURE("testHestonMCForwardStartPrices", payoff, exercise, s, q, r, today,sigma_bs, moneyness[moneyness_index], reset, analyticPrice, mcPrice, mcError, mcForwardStartTolerance[type_index][moneyness_index]);}}// Test 2: Using an arbitrary Heston model, check that prices match semi-analytical// Heston prices when reset date is t=0v0 = sigma_bs * sigma_bs;kappa = 1.0;theta = 0.08;sigma = 0.39;rho = -0.93;reset = today;ext::shared_ptr<HestonProcess> hestonProcessSmile(new HestonProcess(rTS, qTS, Handle<Quote>(spot), v0, kappa, theta, sigma, rho));ext::shared_ptr<HestonModel> hestonModel(ext::make_shared<HestonModel>(hestonProcessSmile));ext::shared_ptr<PricingEngine> analyticHestonEngine(ext::make_shared<AnalyticHestonEngine>(hestonModel, 96));ext::shared_ptr<PricingEngine> mcEngineSmile =MakeMCForwardEuropeanHestonEngine<LowDiscrepancy>(hestonProcessSmile).withSteps(timeSteps).withSamples(numberOfSamples).withSeed(mcSeed);ext::shared_ptr<AnalyticHestonForwardEuropeanEngine> analyticForwardHestonEngine(new AnalyticHestonForwardEuropeanEngine(hestonProcessSmile));for (Size moneyness_index = 0; moneyness_index < LENGTH(moneyness); ++moneyness_index) {Real strike = s * moneyness[moneyness_index];ext::shared_ptr<StrikedTypePayoff> vanillaPayoff(new PlainVanillaPayoff(optionTypes[type_index], strike));VanillaOption vanillaOption(vanillaPayoff, exercise);ForwardVanillaOption forwardOption(moneyness[moneyness_index], reset, payoff, exercise);vanillaOption.setPricingEngine(analyticHestonEngine);Real analyticPrice = vanillaOption.NPV();forwardOption.setPricingEngine(mcEngineSmile);Real mcPrice = forwardOption.NPV();Real mcError = relativeError(analyticPrice, mcPrice, s);auto tolerance = tol[type_index][moneyness_index];if (mcError > tolerance) {REPORT_FAILURE("testHestonMCPrices", vanillaPayoff, exercise, s, q, r, today,sigma_bs, moneyness[moneyness_index], reset, analyticPrice, mcPrice, mcError,tolerance);}// T=0, testing the Analytic Pricer's T=0 analytical solutionforwardOption.setPricingEngine(analyticForwardHestonEngine);Real hestonAnalyticPrice = forwardOption.NPV();Real analyticError = relativeError(analyticPrice, hestonAnalyticPrice, s);if (analyticError > analyticTolerance) {REPORT_FAILURE("testHestonAnalyticForwardStartPrices", vanillaPayoff, exercise, s, q,r, today, sigma_bs, moneyness[moneyness_index], reset, analyticPrice,hestonAnalyticPrice, analyticError, analyticTolerance);}}}
}void ForwardOptionTest::testHestonAnalyticalVsMCPrices() {BOOST_TEST_MESSAGE("Testing Heston analytic vs MC prices...");Option::Type optionTypes[] = { Option::Call, Option::Put };Real tol[][6] = {{0.002,   // Call, moneyness=0.8, CV:false0.002,   // Call, moneyness=0.8, CV:true0.001,   // Call, moneyness=1.0, CV:false0.001,   // Call, moneyness=1.8, CV:true0.001,   // Call, moneyness=1.2, CV:false0.001},  // Call, moneyness=1.2, CV:true{0.001,   // Put, moneyness=0.8, CV:false0.001,   // Put, moneyness=0.8, CV:true0.003,   // Put, moneyness=1.0, CV:false0.003,   // Put, moneyness=1.0, CV:true0.003,   // Put, moneyness=1.2, CV:false0.003}}; // Put, moneyness=1.2, CV:truefor (Size option_type_index = 0; option_type_index < LENGTH(optionTypes); ++option_type_index) {Size timeSteps = 50;Size numberOfSamples = 5000;Size mcSeed = 42;Real q = 0.03;Real r = 0.005;Real s = 100;Real vol = 0.3;Real v0 = vol * vol;Real kappa = 11.35;Real theta = 0.022;Real sigma = 0.618;Real rho = -0.5;DayCounter dc = Actual360();SavedSettings backup;Date today = Settings::instance().evaluationDate();Date exDate = today + 1 * Years;ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));Date reset = today + 6 * Months;ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(optionTypes[option_type_index], 0.0));ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(s));ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(q));Handle<YieldTermStructure> qTS(flatRate(qRate, dc));ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(r));Handle<YieldTermStructure> rTS(flatRate(rRate, dc));ext::shared_ptr<HestonProcess> hestonProcess(new HestonProcess(rTS, qTS, Handle<Quote>(spot), v0, kappa, theta, sigma, rho));ext::shared_ptr<PricingEngine> mcEngine =MakeMCForwardEuropeanHestonEngine<PseudoRandom>(hestonProcess).withSteps(timeSteps).withSamples(numberOfSamples).withSeed(mcSeed);ext::shared_ptr<PricingEngine> mcEngineCv =MakeMCForwardEuropeanHestonEngine<PseudoRandom>(hestonProcess).withSteps(timeSteps).withSamples(numberOfSamples).withSeed(mcSeed).withControlVariate(true);ext::shared_ptr<AnalyticHestonForwardEuropeanEngine> analyticEngine(new AnalyticHestonForwardEuropeanEngine(hestonProcess));Real moneyness[] = { 0.8, 1.0, 1.2 };for (Size tol_2nd_index = 0; tol_2nd_index < LENGTH(moneyness); ++tol_2nd_index) {auto m = moneyness[tol_2nd_index];ForwardVanillaOption option(m, reset, payoff, exercise);option.setPricingEngine(analyticEngine);Real analyticPrice = option.NPV();option.setPricingEngine(mcEngine);Real mcPrice = option.NPV();Real error = relativeError(analyticPrice, mcPrice, s);auto tolerance = tol[option_type_index][tol_2nd_index];if (error > tolerance) {REPORT_FAILURE("testHestonMCVsAnalyticPrices", payoff, exercise, s, q, r, today, vol,m, reset, analyticPrice, mcPrice, error, tolerance);}option.setPricingEngine(mcEngineCv);Real mcPriceCv = option.NPV();Real errorCv = relativeError(analyticPrice, mcPriceCv, s);tolerance = tol[option_type_index][++tol_2nd_index];if (errorCv > tolerance) {REPORT_FAILURE("testHestonMCControlVariateVsAnalyticPrices", payoff, exercise, s, q,r, today, vol, m, reset, analyticPrice, mcPrice, errorCv,tolerance);}}}
}test_suite* ForwardOptionTest::suite(SpeedLevel speed) {auto* suite = BOOST_TEST_SUITE("Forward option tests");suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testValues));suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testGreeks));suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testPerformanceValues));suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testPerformanceGreeks));suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testGreeksInitialization));suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testMCPrices));suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testHestonMCPrices));if (speed <= Fast) {suite->add(QUANTLIB_TEST_CASE(&ForwardOptionTest::testHestonAnalyticalVsMCPrices));}return suite;
}
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本文章博客地址：https://cplusplus.blog.csdn.net/article/details/128363854
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