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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003, 2004 Ferdinando Ametrano
Copyright (C) 2003 RiskMap srl
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/reference/license.html>.
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 "covariance.hpp"
#include "utilities.hpp"
#include <ql/MonteCarlo/getcovariance.hpp>
#include <ql/Math/pseudosqrt.hpp>
#include <ql/Math/sequencestatistics.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
QL_BEGIN_TEST_LOCALS(CovarianceTest)
Real norm(const Matrix& m) {
Real sum = 0.0;
for (Size i=0; i<m.rows(); i++)
for (Size j=0; j<m.columns(); j++)
sum += m[i][j]*m[i][j];
return std::sqrt(sum);
}
QL_END_TEST_LOCALS(CovarianceTest)
void CovarianceTest::testSalvagingCorrelation() {
BOOST_MESSAGE("Testing correlation-salvaging algorithms...");
Real expected, calculated;
Size n = 3;
Matrix badCorr(n, n);
badCorr[0][0] = 1.0; badCorr[0][1] = 0.9; badCorr[0][2] = 0.7;
badCorr[1][0] = 0.9; badCorr[1][1] = 1.0; badCorr[1][2] = 0.3;
badCorr[2][0] = 0.7; badCorr[2][1] = 0.3; badCorr[2][2] = 1.0;
Matrix goodCorr(n, n);
goodCorr[0][0] = goodCorr[1][1] = goodCorr[2][2] = 1.00000000000;
goodCorr[0][1] = goodCorr[1][0] = 0.894024408508599;
goodCorr[0][2] = goodCorr[2][0] = 0.696319066114392;
goodCorr[1][2] = goodCorr[2][1] = 0.300969036104592;
Matrix b = pseudoSqrt(badCorr, SalvagingAlgorithm::Spectral);
// Matrix b = pseudoSqrt(badCorr, Hypersphere);
Matrix calcCorr = b * transpose(b);
for (Size i=0; i<n; i++) {
for (Size j=0; j<n; j++) {
expected = goodCorr[i][j];
calculated = calcCorr[i][j];
if (std::fabs(calculated-expected) > 1.0e-10)
BOOST_ERROR("SalvagingCorrelation with spectral alg "
<< "cor[" << i << "][" << j << "]:\n"
<< std::setprecision(10)
<< " calculated: " << calculated << "\n"
<< " expected: " << expected);
}
}
Matrix badCov(n, n);
badCov[0][0] = 0.04000; badCov[0][1] = 0.03240; badCov[0][2] = 0.02240;
badCov[1][0] = 0.03240; badCov[1][1] = 0.03240; badCov[1][2] = 0.00864;
badCov[2][0] = 0.02240; badCov[2][1] = 0.00864; badCov[2][2] = 0.02560;
b = pseudoSqrt(badCov, SalvagingAlgorithm::Spectral);
Matrix goodCov = b * transpose(b);
Real error = norm(goodCov-badCov);
if (error > 4.0e-4)
BOOST_ERROR(
QL_SCIENTIFIC << error
<< " error while salvaging covariance matrix with spectral alg\n"
<< QL_FIXED
<< "input matrix:\n" << badCov
<< "salvaged matrix:\n" << goodCov);
}
void CovarianceTest::testCovariance() {
BOOST_MESSAGE("Testing covariance and correlation calculations...");
Real data00[] = { 3.0, 9.0 };
Real data01[] = { 2.0, 7.0 };
Real data02[] = { 4.0, 12.0 };
Real data03[] = { 5.0, 15.0 };
Real data04[] = { 6.0, 17.0 };
Real* data[5] = { data00, data01, data02, data03, data04 };
std::vector<Real> weights(LENGTH(data), 1.0);
Size i, j, n = LENGTH(data00);
Matrix expCor(n, n);
expCor[0][0] = 1.0000000000000000; expCor[0][1] = 0.9970544855015813;
expCor[1][0] = 0.9970544855015813; expCor[1][1] = 1.0000000000000000;
SequenceStatistics<> s(n);
std::vector<Real> temp(n);
for (i = 0; i<LENGTH(data); i++) {
for (j=0; j<n; j++) {
temp[j]= data[i][j];
}
s.add(temp, weights[i]);
}
std::vector<Real> m = s.mean();
std::vector<Real> std = s.standardDeviation();
Matrix calcCov = s.covariance();
Matrix calcCor = s.correlation();
Matrix expCov(n, n);
for (i=0; i<n; i++) {
expCov[i][i] = std[i]*std[i];
for (j=0; j<i; j++) {
expCov[i][j] = expCov[j][i] = expCor[i][j]*std[i]*std[j];
}
}
Real expected, calculated;
for (i=0; i<n; i++) {
for (j=0; j<n; j++) {
expected = expCor[i][j];
calculated = calcCor[i][j];
if (std::fabs(calculated-expected) > 1.0e-10)
BOOST_ERROR("SequenceStatistics "
<< "cor[" << i << "][" << j << "]:\n"
<< std::setprecision(10)
<< " calculated: " << calculated << "\n"
<< " expected: " << expected);
expected = expCov[i][j];
calculated = calcCov[i][j];
if (std::fabs(calculated-expected) > 1.0e-10)
BOOST_ERROR("SequenceStatistics "
<< "cov[" << i << "][" << j << "]:\n"
<< std::setprecision(10)
<< " calculated: " << calculated << "\n"
<< " expected: " << expected);
}
}
calcCov = getCovariance(std.begin(), std.end(), expCor);
for (i=0; i<n; i++) {
for (j=0; j<n; j++) {
Real calculated = calcCov[i][j],
expected = expCov[i][j];
if (std::fabs(calculated-expected) > 1.0e-10) {
BOOST_ERROR("getCovariance "
<< "cov[" << i << "][" << j << "]:\n"
<< std::setprecision(10)
<< " calculated: " << calculated << "\n"
<< " expected: " << expected);
}
}
}
CovarianceDecomposition covDecomposition(expCov);
calcCor = covDecomposition.correlationMatrix();
Array calcStd = covDecomposition.standardDeviations();
for (i=0; i<n; i++) {
calculated = calcStd[i];
expected = std[i];
if (std::fabs(calculated-expected) > 1.0e-16) {
BOOST_ERROR("CovarianceDecomposition "
<< "standardDev[" << i << "]:\n"
<< std::setprecision(16) << QL_SCIENTIFIC
<< " calculated: " << calculated << "\n"
<< " expected: " << expected);
}
for (j=0; j<n; j++) {
calculated = calcCor[i][j];
expected = expCor[i][j];
if (std::fabs(calculated-expected) > 1.0e-14) {
BOOST_ERROR("\nCovarianceDecomposition "
<< "corr[" << i << "][" << j << "]:\n"
<< std::setprecision(14) << QL_SCIENTIFIC
<< " calculated: " << calculated << "\n"
<< " expected: " << expected);
}
}
}
}
test_suite* CovarianceTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Covariance/correlation tests");
suite->add(BOOST_TEST_CASE(&CovarianceTest::testSalvagingCorrelation));
suite->add(BOOST_TEST_CASE(&CovarianceTest::testCovariance));
return suite;
}
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