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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Roland Lichters
Copyright (C) 2009 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/credit/randomdefaultmodel.hpp>
#include <ql/math/solvers1d/bisection.hpp>
#include <ql/math/solvers1d/brent.hpp>
#include <utility>
using namespace std;
namespace QuantLib {
namespace {
// Utility for the numerical solver
class Root {
public:
Root(Handle<DefaultProbabilityTermStructure> dts, Real pd)
: dts_(std::move(dts)), pd_(pd) {}
Real operator()(Real t) const {
QL_REQUIRE(t >= 0.0, "GaussianRandomDefaultModel: internal error, t < 0 ("
<< t << ") during root searching.");
return dts_->defaultProbability(t, true) - pd_;
}
private:
const Handle<DefaultProbabilityTermStructure> dts_;
Real pd_;
};
}
GaussianRandomDefaultModel::GaussianRandomDefaultModel(
const ext::shared_ptr<Pool>& pool,
const std::vector<DefaultProbKey>& defaultKeys,
const Handle<OneFactorCopula>& copula,
Real accuracy,
long seed)
: RandomDefaultModel(pool, defaultKeys), copula_(copula), accuracy_(accuracy), seed_(seed),
rsg_(PseudoRandom::make_sequence_generator(pool->size() + 1, seed)) {
registerWith(copula);
}
void GaussianRandomDefaultModel::reset() {
Size dim = pool_->size() + 1;
rsg_ = PseudoRandom::make_sequence_generator(dim, seed_);
}
void GaussianRandomDefaultModel::nextSequence(Real tmax) {
const std::vector<Real>& values = rsg_.nextSequence().value;
Real a = sqrt(copula_->correlation());
for (Size j = 0; j < pool_->size(); j++) {
const string name = pool_->names()[j];
const Handle<DefaultProbabilityTermStructure>&
dts = pool_->get(name).defaultProbability(defaultKeys_[j]);
Real y = a * values[0] + sqrt(1-a*a) * values[j+1];
Real p = CumulativeNormalDistribution()(y);
if (dts->defaultProbability(tmax) < p)
pool_->setTime(name, tmax + 1);
else {
// we know there is a zero of f(t) = dts->defaultProbability(t) - p in [0, tmax]
try {
// try bracketing the root and find it with Brent
Brent brent;
brent.setLowerBound(0.0);
brent.setUpperBound(tmax);
pool_->setTime(name, brent.solve(Root(dts, p), accuracy_, tmax / 2.0, 1.0));
} catch (...) {
// if Brent fails, use Bisection, this is guaranteed to find the root
pool_->setTime(
name, Bisection().solve(Root(dts, p), accuracy_, tmax / 2.0, 0.0, tmax));
}
}
}
}
}
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