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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 RiskMap srl
Copyright (C) 2011 Ferdinando Ametrano
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/distributions/normaldistribution.hpp>
#include <ql/methods/finitedifferences/dzero.hpp>
#include <ql/methods/finitedifferences/dplusdminus.hpp>
#include <ql/methods/finitedifferences/bsmoperator.hpp>
#include <ql/methods/finitedifferences/pdebsm.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/utilities/dataformatters.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(OperatorTests)
BOOST_AUTO_TEST_CASE(testTridiagonal) {
BOOST_TEST_MESSAGE("Testing tridiagonal operator...");
Size n = 8; // can use 3 for easier debugging
TridiagonalOperator T(n);
T.setFirstRow(1.0, 2.0);
T.setMidRows( 0.0, 2.0, 0.0);
T.setLastRow( 2.0, 1.0);
Array original(n, 1.0);
Array intermediate = T.applyTo(original);
Array final(intermediate);
T.solveFor(final, final);
for (Size i=0; i<n; ++i) {
if (final[i]!=original[i])
BOOST_FAIL("\n applyTo + solveFor does not equal identity:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n inverse transformed vector: " << final);
}
final = Array(n, 0.0);
Array temp(intermediate);
T.solveFor(temp, final);
for (Size i=0; i<n; ++i) {
if (temp[i]!=intermediate[i])
BOOST_FAIL("\n solveFor altered rhs:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n altered transformed vector: " << temp <<
"\n inverse transformed vector: " << final);
}
for (Size i=0; i<n; ++i) {
if (final[i]!=original[i])
BOOST_FAIL("\n applyTo + solveFor does not equal identity:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n inverse transformed vector: " << final);
}
final = T.solveFor(temp);
for (Size i=0; i<n; ++i) {
if (temp[i]!=intermediate[i])
BOOST_FAIL("\n solveFor altered rhs:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n altered transformed vector: " << temp <<
"\n inverse transformed vector: " << final);
}
for (Size i=0; i<n; ++i) {
if (final[i]!=original[i])
BOOST_FAIL("\n applyTo + solveFor does not equal identity:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n inverse transformed vector: " << final);
}
Real delta, error = 0.0, tolerance = 1e-9;
final = T.SOR(temp, tolerance);
for (Size i=0; i<n; ++i) {
delta = final[i]-original[i];
error += delta * delta;
if (temp[i]!=intermediate[i])
BOOST_FAIL("\n SOR altered rhs:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n altered transformed vector: " << temp <<
"\n inverse transformed vector: " << final);
}
if (error>tolerance)
BOOST_FAIL("\n applyTo + SOR does not equal identity:"
"\n original vector: " << original <<
"\n transformed vector: " << intermediate <<
"\n inverse transformed vector: " << final <<
"\n error: " << error <<
"\n tolerance: " << tolerance);
}
BOOST_AUTO_TEST_CASE(testConsistency) {
BOOST_TEST_MESSAGE("Testing differential operators...");
Real average = 0.0, sigma = 1.0;
NormalDistribution normal(average,sigma);
CumulativeNormalDistribution cum(average,sigma);
Real xMin = average - 4*sigma,
xMax = average + 4*sigma;
Size N = 10001;
Real h = (xMax-xMin)/(N-1);
Array x(N), y(N), yi(N), yd(N), temp(N), diff(N);
Size i;
for (i=0; i<N; i++)
x[i] = xMin+h*i;
std::transform(x.begin(),x.end(),y.begin(),normal);
std::transform(x.begin(),x.end(),yi.begin(),cum);
for (i=0; i<x.size(); i++)
yd[i] = normal.derivative(x[i]);
// define the differential operators
DZero D(N,h);
DPlusDMinus D2(N,h);
// check that the derivative of cum is Gaussian
temp = D.applyTo(yi);
std::transform(y.begin(), y.end(), temp.begin(), diff.begin(), std::minus<>());
Real e = norm(diff.begin(), diff.end(), h);
if (e > 1.0e-6) {
BOOST_FAIL("norm of 1st derivative of cum minus Gaussian: " << e
<< "\ntolerance exceeded");
}
// check that the second derivative of cum is normal.derivative
temp = D2.applyTo(yi);
std::transform(yd.begin(), yd.end(), temp.begin(), diff.begin(), std::minus<>());
e = norm(diff.begin(), diff.end(), h);
if (e > 1.0e-4) {
BOOST_FAIL("norm of 2nd derivative of cum minus Gaussian derivative: "
<< e << "\ntolerance exceeded");
}
}
BOOST_AUTO_TEST_CASE(testBSMOperatorConsistency) {
BOOST_TEST_MESSAGE("Testing consistency of BSM operators...");
QL_DEPRECATED_DISABLE_WARNING
Array grid(10);
Real price = 20.0;
Real factor = 1.1;
Size i;
for (i = 0; i < grid.size(); i++) {
grid[i] = price;
price *= factor;
}
Real dx = std::log(factor);
Rate r = 0.05;
Rate q = 0.01;
Volatility sigma = 0.5;
BSMOperator ref(grid.size(), dx, r, q, sigma);
DayCounter dc = Actual360();
Date today = Date::todaysDate();
Date exercise = today + 2*Years;
Time residualTime = dc.yearFraction(today,exercise);
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, q, dc);
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, r, dc);
ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, sigma, dc);
ext::shared_ptr<GeneralizedBlackScholesProcess> stochProcess(
new GeneralizedBlackScholesProcess(
Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
Handle<BlackVolTermStructure>(volTS)));
PdeOperator<PdeBSM> op2(grid, stochProcess, residualTime);
Real tolerance = 1.0e-6;
Array lderror = ref.lowerDiagonal() - op2.lowerDiagonal();
Array derror = ref.diagonal() - op2.diagonal();
Array uderror = ref.upperDiagonal() - op2.upperDiagonal();
for (i=2; i<grid.size()-2; i++) {
if (std::fabs(lderror[i]) > tolerance ||
std::fabs(derror[i]) > tolerance ||
std::fabs(uderror[i]) > tolerance) {
BOOST_FAIL("inconsistency between BSM operators:\n"
<< io::ordinal(i) << " row:\n"
<< "expected: "
<< ref.lowerDiagonal()[i] << ", "
<< ref.diagonal()[i] << ", "
<< ref.upperDiagonal()[i] << "\n"
<< "calculated: "
<< op2.lowerDiagonal()[i] << ", "
<< op2.diagonal()[i] << ", "
<< op2.upperDiagonal()[i]);
}
}
QL_DEPRECATED_ENABLE_WARNING
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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