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/*
Copyright (C) 2001, 2002 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 ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
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.
*/
/*! \file g2.hpp
\brief Two-additive-factor Gaussian Model G2++
\fullpath
ql/InterestRateModelling/TwoFactorModels/%g2.hpp
*/
// $Id: g2.hpp,v 1.9 2002/03/06 07:16:06 sadrejeb Exp $
#ifndef quantlib_two_factor_models_g2_h
#define quantlib_two_factor_models_g2_h
#include "ql/InterestRateModelling/twofactormodel.hpp"
namespace QuantLib {
namespace InterestRateModelling {
class G2 : public TwoFactorModel, public AffineModel {
public:
G2(const RelinkableHandle<TermStructure>& termStructure);
virtual ~G2() {}
double discountBondOption(Option::Type type,
double strike,
Time maturity,
Time bondMaturity) const;
protected:
virtual void generateParameters() {
phi_ = G2FittingParameter(termStructure(),
a(), sigma(), b(), eta(), rho());
}
private:
class Process : public TwoFactorModel::ShortRateProcess {
public:
Process(
const Parameter& fitting,
double a, double sigma, double b, double eta, double rho)
: ShortRateProcess(
Handle<DiffusionProcess>(
new OrnsteinUhlenbeckProcess(a, sigma)),
Handle<DiffusionProcess>(
new OrnsteinUhlenbeckProcess(b, eta)),
rho), fitting_(fitting) {}
virtual Rate shortRate(Time t, double x, double y) const {
return fitting_(t) + x + y;
}
private:
Parameter fitting_;
};
class G2FittingParameter : public TermStructureFittingParameter {
public:
class G2Impl : public Parameter::ParameterImpl {
public:
G2Impl(const RelinkableHandle<TermStructure>& termStructure,
double a, double sigma, double b, double eta,
double rho)
: termStructure_(termStructure),
a_(a), sigma_(sigma), b_(b), eta_(eta), rho_(rho) {}
virtual ~G2Impl() {}
double value(const Array& params, Time t) const {
double forward = termStructure_->forward(t);
double temp1 = sigma_*(1.0-QL_EXP(a_*t))/a_;
double temp2 = eta_*(1.0-QL_EXP(b_*t))/b_;
double value = 0.5*temp1*temp1 + 0.5*temp2*temp2 +
rho_*temp1*temp2 + forward;
return value;
}
private:
RelinkableHandle<TermStructure> termStructure_;
double a_, sigma_, b_, eta_, rho_;
};
G2FittingParameter(
const RelinkableHandle<TermStructure>& termStructure,
double a, double sigma, double b, double eta, double rho)
: TermStructureFittingParameter(Handle<ParameterImpl>(
new G2Impl(termStructure, a, sigma, b, eta, rho))) {}
};
inline double sigmaP(Time t, Time s) const {
double temp = 1.0 - QL_EXP(-(a()+b())*t);
double temp1 = 1.0 - QL_EXP(-a()*(s-t));
double temp2 = 1.0 - QL_EXP(-b()*(s-t));
double a3 = a()*a()*a();
double b3 = b()*b()*b();
double sigma2 = sigma()*sigma();
double eta2 = eta()*eta();
double value =
0.5*sigma2*temp1*temp1*(1.0 - QL_EXP(-2.0*a()*t))/a3 +
0.5*eta2*temp2*temp2*(1.0 - QL_EXP(-2.0*b()*t))/b3 +
2.0*rho()*sigma()*eta()/(a()*b()*(a()+b()))*
temp1*temp2*temp;
return QL_SQRT(value);
}
Parameter& a_;
Parameter& sigma_;
Parameter& b_;
Parameter& eta_;
Parameter& rho_;
Parameter& phi_;
double a() const { return a_(0.0); }
double sigma() const { return sigma_(0.0); }
double b() const { return b_(0.0); }
double eta() const { return eta_(0.0); }
double rho() const { return rho_(0.0); }
class OwnConstraint;
};
}
}
#endif
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