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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Klaus Spanderen
Copyright (C) 2007 StatPro Italia srl
Copyright (C) 2015 Thema Consulting SA
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 "preconditions.hpp"
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/instruments/vanillaoption.hpp>
#include <ql/methods/montecarlo/lsmbasissystem.hpp>
#include <ql/pricingengines/mclongstaffschwartzengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/pricingengines/vanilla/mcamericanengine.hpp>
#include <ql/processes/stochasticprocessarray.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <utility>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(MCLongstaffSchwartzEngineTests)
class AmericanMaxPathPricer : public EarlyExercisePathPricer<MultiPath> {
public:
explicit AmericanMaxPathPricer(ext::shared_ptr<Payoff> payoff)
: payoff_(std::move(payoff)) {}
StateType state(const MultiPath& path, Size t) const override {
Array tmp(path.assetNumber());
for (Size i=0; i<path.assetNumber(); ++i) {
tmp[i]=path[i][t];
}
return tmp;
}
Real operator()(const MultiPath& path, Size t) const override {
const Array tmp = state(path, t);
return (*payoff_)(*std::max_element(tmp.begin(), tmp.end()));
}
std::vector<std::function<Real(StateType)> > basisSystem() const override {
return LsmBasisSystem::multiPathBasisSystem(2, 2,
LsmBasisSystem::Monomial);
}
protected:
const ext::shared_ptr<Payoff> payoff_;
};
template <class RNG>
class MCAmericanMaxEngine
: public MCLongstaffSchwartzEngine<VanillaOption::engine,
MultiVariate,RNG>{
public:
MCAmericanMaxEngine(const ext::shared_ptr<StochasticProcessArray>& processes,
Size timeSteps,
Size timeStepsPerYear,
bool brownianbridge,
bool antitheticVariate,
bool controlVariate,
Size requiredSamples,
Real requiredTolerance,
Size maxSamples,
BigNatural seed,
Size nCalibrationSamples = Null<Size>())
: MCLongstaffSchwartzEngine<VanillaOption::engine,
MultiVariate,RNG>(processes,
timeSteps,
timeStepsPerYear,
brownianbridge,
antitheticVariate,
controlVariate,
requiredSamples,
requiredTolerance,
maxSamples,
seed, nCalibrationSamples)
{ }
protected:
ext::shared_ptr<LongstaffSchwartzPathPricer<MultiPath> > lsmPathPricer() const override {
ext::shared_ptr<StochasticProcessArray> processArray =
ext::dynamic_pointer_cast<StochasticProcessArray>(this->process_);
QL_REQUIRE(processArray && processArray->size() > 0,
"Stochastic process array required");
ext::shared_ptr<GeneralizedBlackScholesProcess> process =
ext::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
processArray->process(0));
QL_REQUIRE(process, "generalized Black-Scholes proces required");
ext::shared_ptr<AmericanMaxPathPricer> earlyExercisePathPricer(
new AmericanMaxPathPricer(this->arguments_.payoff));
return ext::make_shared<LongstaffSchwartzPathPricer<MultiPath> > (
this->timeGrid(),
earlyExercisePathPricer,
process->riskFreeRate().currentLink());
}
};
BOOST_AUTO_TEST_CASE(testAmericanOption, *precondition(if_speed(Fast))) {
BOOST_TEST_MESSAGE("Testing Monte-Carlo pricing of American options...");
// most of the example taken from the EquityOption.cpp
const Option::Type type(Option::Put);
const Real underlying = 36;
const Spread dividendYield = 0.00;
const Rate riskFreeRate = 0.06;
const Volatility volatility = 0.20;
const Date todaysDate(15, May, 1998);
const Date settlementDate(17, May, 1998);
Settings::instance().evaluationDate() = todaysDate;
const Date maturity(17, May, 1999);
const DayCounter dayCounter = Actual365Fixed();
ext::shared_ptr<Exercise> americanExercise(
new AmericanExercise(settlementDate, maturity));
// 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)));
// expected results for exercise probability, evaluated with third-party
// product (using Cox-Rubinstein binomial tree)
Matrix expectedExProb(2, 3);
expectedExProb[0][0] = 0.48013; // (price: 2.105)
expectedExProb[0][1] = 0.51678; // (price: 3.451)
expectedExProb[0][2] = 0.54598; // (price: 4.807)
expectedExProb[1][0] = 0.75549; // (price: 4.505)
expectedExProb[1][1] = 0.67569; // (price: 5.764)
expectedExProb[1][2] = 0.65562; // (price: 7.138)
LsmBasisSystem::PolynomialType polynomialTypes[]
= { LsmBasisSystem::Monomial, LsmBasisSystem::Laguerre,
LsmBasisSystem::Hermite, LsmBasisSystem::Hyperbolic,
LsmBasisSystem::Chebyshev2nd };
for (Integer i=0; i<2; ++i) {
for (Integer j=0; j<3; ++j) {
Handle<BlackVolTermStructure> flatVolTS(
ext::shared_ptr<BlackVolTermStructure>(
new BlackConstantVol(settlementDate, NullCalendar(),
volatility+0.1*j, dayCounter)));
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(type, underlying+4*i));
Handle<Quote> underlyingH(
ext::shared_ptr<Quote>(new SimpleQuote(underlying)));
ext::shared_ptr<GeneralizedBlackScholesProcess>
stochasticProcess(new GeneralizedBlackScholesProcess(
underlyingH, flatDividendTS,
flatTermStructure, flatVolTS));
VanillaOption americanOption(payoff, americanExercise);
ext::shared_ptr<PricingEngine> mcengine =
MakeMCAmericanEngine<PseudoRandom>(stochasticProcess)
.withSteps(75)
.withAntitheticVariate()
.withAbsoluteTolerance(0.02)
.withSeed(42)
.withPolynomialOrder(3)
.withBasisSystem(polynomialTypes[0*(i*3+j)%std::size(polynomialTypes)]);
americanOption.setPricingEngine(mcengine);
const Real calculated = americanOption.NPV();
const Real errorEstimate = americanOption.errorEstimate();
const Real exerciseProbability =
americanOption.result<QuantLib::Real>("exerciseProbability");
americanOption.setPricingEngine(ext::shared_ptr<PricingEngine>(
new FdBlackScholesVanillaEngine(stochasticProcess, 401, 200)));
const Real expected = americanOption.NPV();
// Check price
if (std::fabs(calculated - expected) > 2.34*errorEstimate) {
BOOST_ERROR("Failed to reproduce american option prices"
<< "\n expected: " << expected
<< "\n calculated: " << calculated
<< " +/- " << errorEstimate);
}
// Check exercise probability (tolerance 1.5%)
if (std::fabs(exerciseProbability - expectedExProb[i][j]) > 0.015) {
BOOST_ERROR("Failed to reproduce american option "
<< "exercise probability"
<< "\n expected: " << expectedExProb[i][j]
<< "\n calculated: " << exerciseProbability);
}
}
}
}
BOOST_AUTO_TEST_CASE(testAmericanMaxOption) {
// reference values taken from
// "Monte Carlo Methods in Financial Engineering",
// by Paul Glasserman, 2004 Springer Verlag, p. 462
BOOST_TEST_MESSAGE("Testing Monte-Carlo pricing of American max options...");
// most of the example taken from the EquityOption.cpp
const Option::Type type(Option::Call);
const Real strike = 100;
const Spread dividendYield = 0.10;
const Rate riskFreeRate = 0.05;
const Volatility volatility = 0.20;
const Date todaysDate(15, May, 1998);
const Date settlementDate(17, May, 1998);
Settings::instance().evaluationDate() = todaysDate;
const Date maturity(16, May, 2001);
const DayCounter dayCounter = Actual365Fixed();
ext::shared_ptr<Exercise> americanExercise(
new AmericanExercise(settlementDate, maturity));
// 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, NullCalendar(),
volatility, dayCounter)));
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(type, strike));
RelinkableHandle<Quote> underlyingH;
ext::shared_ptr<GeneralizedBlackScholesProcess> stochasticProcess(new
GeneralizedBlackScholesProcess(
underlyingH, flatDividendTS, flatTermStructure, flatVolTS));
const Size numberAssets = 2;
Matrix corr(numberAssets, numberAssets, 0.0);
std::vector<ext::shared_ptr<StochasticProcess1D> > v;
for (Size i=0; i<numberAssets; ++i) {
v.push_back(stochasticProcess);
corr[i][i] = 1.0;
}
ext::shared_ptr<StochasticProcessArray> process(
new StochasticProcessArray(v, corr));
VanillaOption americanMaxOption(payoff, americanExercise);
ext::shared_ptr<PricingEngine> mcengine(
new MCAmericanMaxEngine<PseudoRandom>(process, 25, Null<Size>(), false,
true, false, 4096,
Null<Real>(), Null<Size>(),
42, 1024));
americanMaxOption.setPricingEngine(mcengine);
const Real expected[] = {8.08, 13.90, 21.34};
for (Size i = 0; i < 3; ++i) {
const Real underlying = 90.0 + i*10.0;
underlyingH.linkTo(
ext::shared_ptr<Quote>(new SimpleQuote(underlying)));
const Real calculated = americanMaxOption.NPV();
const Real errorEstimate = americanMaxOption.errorEstimate();
if (std::fabs(calculated - expected[i]) > 2.34*errorEstimate) {
BOOST_ERROR("Failed to reproduce american option prices"
<< "\n expected: " << expected[i]
<< "\n calculated: " << calculated
<< " +/- " << errorEstimate);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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