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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
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/models/shortrate/onefactormodels/blackkarasinski.hpp>
#include <ql/methods/lattices/trinomialtree.hpp>
#include <ql/math/solvers1d/brent.hpp>
namespace QuantLib {
// Private function used by solver to determine time-dependent parameter
class BlackKarasinski::Helper {
public:
Helper(Size i, Real xMin, Real dx,
Real discountBondPrice,
const ext::shared_ptr<ShortRateTree>& tree)
: size_(tree->size(i)),
dt_(tree->timeGrid().dt(i)),
xMin_(xMin), dx_(dx),
statePrices_(tree->statePrices(i)),
discountBondPrice_(discountBondPrice) {}
Real operator()(Real theta) const {
Real value = discountBondPrice_;
Real x = xMin_;
for (Size j=0; j<size_; j++) {
Real discount = std::exp(-std::exp(theta+x)*dt_);
value -= statePrices_[j]*discount;
x += dx_;
}
return value;
}
private:
Size size_;
Time dt_;
Real xMin_, dx_;
const Array& statePrices_;
Real discountBondPrice_;
};
BlackKarasinski::BlackKarasinski(
const Handle<YieldTermStructure>& termStructure,
Real a, Real sigma)
: OneFactorModel(2), TermStructureConsistentModel(termStructure),
a_(arguments_[0]), sigma_(arguments_[1]) {
a_ = ConstantParameter(a, PositiveConstraint());
sigma_ = ConstantParameter(sigma, PositiveConstraint());
phi_ = TermStructureFittingParameter(termStructure);
registerWith(termStructure);
}
ext::shared_ptr<Lattice>
BlackKarasinski::tree(const TimeGrid& grid) const {
ext::shared_ptr<ShortRateDynamics> numericDynamics(
new Dynamics(phi_, a(), sigma()));
ext::shared_ptr<TrinomialTree> trinomial(
new TrinomialTree(numericDynamics->process(), grid));
ext::shared_ptr<ShortRateTree> numericTree(
new ShortRateTree(trinomial, numericDynamics, grid));
typedef TermStructureFittingParameter::NumericalImpl NumericalImpl;
ext::shared_ptr<NumericalImpl> impl =
ext::dynamic_pointer_cast<NumericalImpl>(phi_.implementation());
impl->reset();
Real value = 1.0;
Real vMin = -50.0;
Real vMax = 50.0;
for (Size i=0; i<(grid.size() - 1); i++) {
Real discountBond = termStructure()->discount(grid[i+1]);
Real xMin = trinomial->underlying(i, 0);
Real dx = trinomial->dx(i);
Helper finder(i, xMin, dx, discountBond, numericTree);
Brent s1d;
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl->set(grid[i], value);
}
return numericTree;
}
ext::shared_ptr<OneFactorModel::ShortRateDynamics>
BlackKarasinski::dynamics() const {
// Calibrate fitting parameter to term structure
Size steps = 50;
ext::shared_ptr<Lattice> lattice = this->tree(
TimeGrid(termStructure()->maxTime(), steps));
ext::shared_ptr<ShortRateDynamics> numericDynamics(
new Dynamics(phi_, a(), sigma()));
return numericDynamics;
}
}
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