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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2018 Klaus Spanderen
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 "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/math/randomnumbers/rngtraits.hpp>
#include <ql/math/integrals/gausslobattointegral.hpp>
#include <ql/math/statistics/generalstatistics.hpp>
#include <ql/pricingengines/vanilla/analyticcevengine.hpp>
#include <ql/pricingengines/vanilla/fdcevvanillaengine.hpp>
#include <ql/methods/finitedifferences/utilities/cevrndcalculator.hpp>
#include <ql/shared_ptr.hpp>
using namespace QuantLib;
using boost::unit_test_framework::test_suite;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(FdCevTests)
class ExpectationFct {
public:
ExpectationFct(const CEVRNDCalculator& calculator, Time t)
: t_(t), calculator_(calculator) { }
Real operator()(Real f) const { return f*calculator_.pdf(f, t_); }
private:
const Time t_;
const CEVRNDCalculator& calculator_;
};
BOOST_AUTO_TEST_CASE(testLocalMartingale) {
BOOST_TEST_MESSAGE(
"Testing local martingale property of CEV process with PDF...");
const Time t = 1.0;
const Real f0 = 2.1;
const Real alpha = 1.75;
const Real betas[] = {-2.4, 0.23, 0.9, 1.1, 1.5};
for (Real beta : betas) {
const CEVRNDCalculator rndCalculator(f0, alpha, beta);
const Real eps = 1e-10;
const Real tol = 100*eps;
const Real upperBound = 10*rndCalculator.invcdf(1-eps, t);
const Real expectationValue = GaussLobattoIntegral(10000, eps)(
ExpectationFct(rndCalculator, t), QL_EPSILON, upperBound);
const Real diff = expectationValue-f0;
if (beta < 1.0 && std::fabs(diff) > tol) {
BOOST_ERROR("CEV process should be a martingale for beta < 1.0"
<< "\n expected: " << f0
<< std::scientific
<< "\n difference " << diff
<< "\n tolerance: " << tol);
}
if (beta > 1.0 && diff > -tol) {
BOOST_ERROR("CEV process should only be a local martingale "
"for beta > 1.0. Expectation is E[F_t|F_0] < F_0"
<< "\n E[F_t|F_0]: " << expectationValue
<< "\n F_0: " << f0);
}
// check local martingale property with Monte-Carlo simulation
const Size nSims = 5000;
const Size nSteps = 2000;
const Real dt = t / nSteps;
const Real sqrtDt = std::sqrt(dt);
GeneralStatistics stat;
const PseudoRandom::rng_type mt(MersenneTwisterUniformRng(42));
if (beta > 1.2) {
for (Size i=0; i < nSims; ++i) {
Real f = f0;
for (Size j=0; j < nSteps; ++j) {
f += alpha * std::pow(f, beta) * mt.next().value * sqrtDt;
f = std::max(0.0, f);
if (f == 0.0) break; // absorbing boundary
}
stat.add(f - f0);
}
const Real calculated = stat.mean();
const Real error = stat.errorEstimate();
if (std::fabs(calculated - diff) > 2.35*error) {
BOOST_ERROR(
"failed to calculate local martingale property "
"by Monte-Carlo Simulation for beta > 1.0. "
<< "\n E[F_t|F_0] : " << expectationValue
<< "\n E_MC[F_t|F_0]: " << calculated + f0
<< "\n error_MC : " << error
<< "\n difference : " << std::fabs(calculated - diff)
<< "\n tolerance : " << 2.35*error);
}
}
}
}
BOOST_AUTO_TEST_CASE(testFdmCevOp) {
BOOST_TEST_MESSAGE(
"Testing FDM constant elasticity of variance (CEV) operator...");
const Date today = Date(22, February, 2018);
const DayCounter dc = Actual365Fixed();
Settings::instance().evaluationDate() = today;
const Date maturityDate = today + Period(12, Months);
const Real strike = 2.3;
const Option::Type optionTypes[] = { Option::Call, Option::Put};
const ext::shared_ptr<Exercise> exercise =
ext::make_shared<EuropeanExercise>(maturityDate);
for (auto optionType : optionTypes) {
const ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::make_shared<PlainVanillaPayoff>(optionType, strike);
const ext::shared_ptr<YieldTermStructure> rTS =
flatRate(today, 0.15, dc);
const Real f0 = 2.1;
const Real alpha = 0.75;
const Real betas[] = { -2.0, -0.5, 0.45, 0.6, 0.9, 1.45 };
for (Real beta : betas) {
VanillaOption option(payoff, exercise);
option.setPricingEngine(ext::make_shared<AnalyticCEVEngine>(
f0, alpha, beta, Handle<YieldTermStructure>(rTS)));
const Real analyticNPV = option.NPV();
const Real eps = 1e-3;
option.setPricingEngine(ext::make_shared<AnalyticCEVEngine>(
f0*(1+eps), alpha, beta, Handle<YieldTermStructure>(rTS)));
const Real analyticUpNPV = option.NPV();
option.setPricingEngine(ext::make_shared<AnalyticCEVEngine>(
f0*(1-eps), alpha, beta, Handle<YieldTermStructure>(rTS)));
const Real analyticDownNPV = option.NPV();
const Real analyticDelta = (analyticUpNPV - analyticDownNPV)
/(2*eps*f0);
option.setPricingEngine(ext::make_shared<FdCEVVanillaEngine>(
f0, alpha, beta, Handle<YieldTermStructure>(rTS),
100, 1000, 1, 1.0, 1e-6));
const Real calculatedNPV = option.NPV();
const Real calculatedDelta = option.delta();
const Real tol = 0.01;
if (std::fabs(calculatedNPV - analyticNPV) > tol
|| std::fabs(calculatedDelta - analyticDelta) > tol) {
BOOST_ERROR(
"failed to calculate vanilla option prices/delta "
<< "\n beta : " << beta
<< "\n option type : "
<< ((payoff->optionType() == Option::Call) ? "Call" : "Put")
<< "\n analytic npv : " << analyticNPV
<< "\n pde npv : " << calculatedNPV
<< "\n npv difference : "
<< std::fabs(calculatedNPV - analyticNPV)
<< "\n tolerance : " << tol
<< "\n analytic delta : " << analyticDelta
<< "\n pde delta : " << calculatedDelta
<< "\n delta difference: "
<< std::fabs(calculatedDelta - analyticDelta)
<< "\n tolerance : " << tol);
}
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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