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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Jose Aparicio
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
<https://www.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 <ql/experimental/math/tcopulapolicy.hpp>
#include <numeric>
#include <algorithm>
namespace QuantLib {
TCopulaPolicy::TCopulaPolicy(
const std::vector<std::vector<Real> >& factorWeights,
const initTraits& vals)
{
for (int tOrder : vals.tOrders) {
// require no T is of order 2 (finite variance)
QL_REQUIRE(tOrder > 2, "Non finite variance T in latent model.");
distributions_.emplace_back(tOrder);
// inverses T variaces used in normalization of the random factors
// For low values of the T order this number is very close to zero
// and it enters the expressions dividing them, which introduces
// numerical errors.
varianceFactors_.push_back(std::sqrt((tOrder - 2.) / tOrder));
}
for (const auto& factorWeight : factorWeights) {
// This ensures the latent model is 'canonical'
QL_REQUIRE(vals.tOrders.size() == factorWeight.size() + 1,
// num factors plus one
"Incompatible number of T functions and number of factors.");
Real factorsNorm = std::inner_product(factorWeight.begin(), factorWeight.end(),
factorWeight.begin(), Real(0.));
QL_REQUIRE(factorsNorm < 1.,
"Non normal random factor combination.");
Real idiosyncFctr = std::sqrt(1.-factorsNorm);
// linear comb factors ajusted for the variance renormalization:
std::vector<Real> normFactorWeights;
normFactorWeights.reserve(factorWeight.size());
for (Size iFactor = 0; iFactor < factorWeight.size(); iFactor++)
normFactorWeights.push_back(factorWeight[iFactor] * varianceFactors_[iFactor]);
// idiosincratic term, all Z factors are assumed identical.
normFactorWeights.push_back(idiosyncFctr * varianceFactors_.back());
latentVarsCumul_.emplace_back(vals.tOrders, normFactorWeights);
latentVarsInverters_.emplace_back(vals.tOrders, normFactorWeights);
}
}
std::vector<Real> TCopulaPolicy::allFactorCumulInverter(
const std::vector<Real>& probs) const
{
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(probs.size()-latentVarsCumul_.size()
== distributions_.size()-1,
"Incompatible sample and latent model sizes");
#endif
std::vector<Real> result(probs.size());
Size indexSystemic = 0;
std::transform(probs.begin(), probs.begin() + varianceFactors_.size()-1,
result.begin(),
[&](Probability p) { return inverseCumulativeDensity(p, indexSystemic++); });
std::transform(probs.begin() + varianceFactors_.size()-1, probs.end(),
result.begin()+ varianceFactors_.size()-1,
[&](Probability p) { return inverseCumulativeZ(p); });
return result;
}
}
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