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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 SunTrust Bank
Copyright (C) 2010 Cavit Hafizoglu
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/shortrate/generalizedhullwhite.hpp>
#include <ql/termstructures/interpolatedcurve.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/methods/lattices/trinomialtree.hpp>
#include <ql/math/solvers1d/brent.hpp>
namespace QuantLib {
namespace {
class PiecewiseLinearCurve : public InterpolatedCurve<Linear> {
public:
PiecewiseLinearCurve(const std::vector<Time>& times,
const std::vector<Real>& data)
: InterpolatedCurve<Linear>(times, data) {
setupInterpolation();
}
Real operator()(Time t) {
return interpolation_(t);
}
};
}
/* Private function used by solver to determine time-dependent parameter
df(r) = [theta(t) - a(t) f(r)]dt + sigma(t) dz
dg = [theta(t) - a(t) g(t)] dt
dx = -a(t) x dt + sigma(t) dz
x = f(r) - g(t)
*/
// Change the overloaded operator to change the model by changing
// the function below
Real fInverse_(Real x) {
return std::exp(x);
}
class GeneralizedHullWhite::Helper {
public:
Helper(const Size i, const Real xMin, const Real dx,
const Real discountBondPrice,
const boost::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()(const Real theta) const {
Real value = discountBondPrice_;
Real x = xMin_;
for (Size j=0; j<size_; j++) {
Real discount = std::exp(- fInverse_(theta+x)*dt_);
value -= statePrices_[j]*discount;
x += dx_;
}
return value;
}
private:
Size size_;
Time dt_;
Real xMin_, dx_;
const Array& statePrices_;
Real discountBondPrice_;
};
GeneralizedHullWhite::GeneralizedHullWhite(
const Handle<YieldTermStructure>& yieldtermStructure,
const std::vector<Date>& speedstructure,
const std::vector<Date>& volstructure)
: OneFactorModel(2), TermStructureConsistentModel(yieldtermStructure),
speedstructure_(speedstructure), volstructure_(volstructure),
a_(arguments_[0]), sigma_(arguments_[1]) {
DayCounter dc = yieldtermStructure->dayCounter();
speedperiods_.push_back(0.0);
for (Size i=0;i<speedstructure.size()-1;i++)
speedperiods_.push_back(dc.yearFraction(speedstructure[0],
speedstructure[i+1]));
a_ = PiecewiseConstantParameter(speedperiods_, PositiveConstraint());
volperiods_.push_back(0.0);
for (Size i=0;i<volstructure.size()-1;i++)
volperiods_.push_back(dc.yearFraction(volstructure[0],
volstructure[i+1]));
sigma_ = PiecewiseConstantParameter(volperiods_, PositiveConstraint());
a_.setParam(0,0.1);
sigma_.setParam(0,0.1);
for (Size i=1; i< a_.size();i++){
a_.setParam(i,0.1*i+0.01);
}
for (Size i=1; i< sigma_.size();i++){
sigma_.setParam(i,0.1*i+0.01);
}
registerWith(yieldtermStructure);
}
GeneralizedHullWhite::GeneralizedHullWhite(
const Handle<YieldTermStructure>& yieldtermStructure,
const std::vector<Date>& speedstructure,
const std::vector<Date>& volstructure,
const std::vector<Real>& speed,
const std::vector<Real>& vol)
: OneFactorModel(2), TermStructureConsistentModel(yieldtermStructure),
speedstructure_(speedstructure),
volstructure_(volstructure),
a_(arguments_[0]), sigma_(arguments_[1]) {
DayCounter dc = yieldtermStructure->dayCounter();
speedperiods_.push_back(0.0);
for (Size i=0;i<speedstructure.size()-1;i++)
speedperiods_.push_back(dc.yearFraction(speedstructure[0],
speedstructure[i+1]));
a_ = PiecewiseConstantParameter(speedperiods_, PositiveConstraint());
volperiods_.push_back(0.0);
for (Size i=0;i<volstructure.size()-1;i++)
volperiods_.push_back(dc.yearFraction(volstructure[0],
volstructure[i+1]));
sigma_ = PiecewiseConstantParameter(volperiods_, PositiveConstraint());
a_.setParam(0,speed[0]);
sigma_.setParam(0,vol[0]);
for (Size i=1; i< sigma_.size();i++) {
sigma_.setParam(i,vol[i-1]);
}
for (Size i=1; i< a_.size();i++) {
a_.setParam(i,speed[i-1]);
}
registerWith(yieldtermStructure);
}
boost::shared_ptr<Lattice> GeneralizedHullWhite::tree(
const TimeGrid& grid) const{
TermStructureFittingParameter phi(termStructure());
boost::shared_ptr<ShortRateDynamics> numericDynamics(
new Dynamics(phi, speed(), vol()));
boost::shared_ptr<TrinomialTree> trinomial(
new TrinomialTree(numericDynamics->process(), grid));
boost::shared_ptr<ShortRateTree> numericTree(
new ShortRateTree(trinomial, numericDynamics, grid));
typedef TermStructureFittingParameter::NumericalImpl NumericalImpl;
boost::shared_ptr<NumericalImpl> impl =
boost::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;
}
boost::function<Real (Time)> GeneralizedHullWhite::speed() const {
std::vector<Real> speedvals;
speedvals.push_back(a_(0.0001));
for (Size i=0;i<a_.size()-1;i++)
speedvals.push_back(
a_(
(speedstructure_[i+1]-speedstructure_[0])/365.0
- 0.00001));
return PiecewiseLinearCurve(speedperiods_, speedvals);
}
boost::function<Real (Time)> GeneralizedHullWhite::vol() const {
std::vector<Real> volvals;
volvals.push_back(sigma_(0.0001));
for (Size i=0;i<sigma_.size()-1;i++)
volvals.push_back(
sigma_(
(speedstructure_[i+1]-speedstructure_[0])/365.0
- 0.00001));
return PiecewiseLinearCurve(volperiods_, volvals);
}
}
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