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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
<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 <ql/experimental/math/tcopulapolicy.hpp>
#include <ql/functional.hpp>
#include <numeric>
#include <algorithm>
namespace QuantLib {
TCopulaPolicy::TCopulaPolicy(
const std::vector<std::vector<Real> >& factorWeights,
const initTraits& vals)
{
for(Size iFactor=0; iFactor<vals.tOrders.size(); iFactor++) {
// require no T is of order 2 (finite variance)
QL_REQUIRE(vals.tOrders[iFactor] > 2,
"Non finite variance T in latent model.");
distributions_.push_back(boost::math::students_t_distribution<>(
vals.tOrders[iFactor]));
// 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(
(vals.tOrders[iFactor]-2.)/vals.tOrders[iFactor]));
}
for(Size iLVar=0; iLVar<factorWeights.size(); iLVar++) {
// This ensures the latent model is 'canonical'
QL_REQUIRE(vals.tOrders.size() == factorWeights[iLVar].size()+1,
// num factors plus one
"Incompatible number of T functions and number of factors.");
Real factorsNorm = std::inner_product(factorWeights[iLVar].begin(),
factorWeights[iLVar].end(), factorWeights[iLVar].begin(), 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;
for(Size iFactor=0; iFactor<factorWeights[iLVar].size(); iFactor++)
normFactorWeights.push_back(factorWeights[iLVar][iFactor] *
varianceFactors_[iFactor]);
// idiosincratic term, all Z factors are assumed identical.
normFactorWeights.push_back(idiosyncFctr * varianceFactors_.back());
latentVarsCumul_.push_back(
CumulativeBehrensFisher(vals.tOrders, normFactorWeights));
latentVarsInverters_.push_back(
InverseCumulativeBehrensFisher(vals.tOrders,
normFactorWeights));
}
}
Disposable<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
using namespace ext::placeholders;
std::vector<Real> result(probs.size());
Size indexSystemic = 0;
std::transform(probs.begin(), probs.begin() + varianceFactors_.size()-1,
result.begin(),
ext::bind(&TCopulaPolicy::inverseCumulativeDensity,
this, _1, indexSystemic++));
std::transform(probs.begin() + varianceFactors_.size()-1, probs.end(),
result.begin()+ varianceFactors_.size()-1,
ext::bind(&TCopulaPolicy::inverseCumulativeZ, this, _1));
return result;
}
}
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