/
extendedcoxingersollross.cpp
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extendedcoxingersollross.cpp
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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
<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/models/shortrate/onefactormodels/extendedcoxingersollross.hpp>
#include <ql/methods/lattices/trinomialtree.hpp>
#include <ql/math/distributions/chisquaredistribution.hpp>
namespace QuantLib {
ExtendedCoxIngersollRoss::ExtendedCoxIngersollRoss(
const Handle<YieldTermStructure>& termStructure,
Real theta, Real k, Real sigma, Real x0,
bool withFellerConstraint)
: CoxIngersollRoss(x0, theta, k, sigma, withFellerConstraint),
TermStructureConsistentModel(termStructure){
generateArguments();
}
ext::shared_ptr<Lattice> ExtendedCoxIngersollRoss::tree(
const TimeGrid& grid) const {
TermStructureFittingParameter phi(termStructure());
ext::shared_ptr<Dynamics> numericDynamics(
new Dynamics(phi, theta(), k(), sigma(), x0()));
ext::shared_ptr<TrinomialTree> trinomial(
new TrinomialTree(numericDynamics->process(), grid, true));
typedef TermStructureFittingParameter::NumericalImpl NumericalImpl;
ext::shared_ptr<NumericalImpl> impl =
ext::dynamic_pointer_cast<NumericalImpl>(phi.implementation());
return ext::shared_ptr<Lattice>(
new ShortRateTree(trinomial, numericDynamics, impl, grid));
}
Real ExtendedCoxIngersollRoss::A(Time t, Time s) const {
Real pt = termStructure()->discount(t);
Real ps = termStructure()->discount(s);
Real value = CoxIngersollRoss::A(t,s)*std::exp(B(t,s)*phi_(t))*
(ps*CoxIngersollRoss::A(0.0,t)*std::exp(-B(0.0,t)*x0()))/
(pt*CoxIngersollRoss::A(0.0,s)*std::exp(-B(0.0,s)*x0()));
return value;
}
Real ExtendedCoxIngersollRoss::discountBondOption(Option::Type type,
Real strike,
Time t, Time s) const {
QL_REQUIRE(strike>0.0, "strike must be positive");
DiscountFactor discountT = termStructure()->discount(t);
DiscountFactor discountS = termStructure()->discount(s);
if (t < QL_EPSILON) {
switch(type) {
case Option::Call:
return std::max<Real>(discountS - strike, 0.0);
case Option::Put:
return std::max<Real>(strike - discountS, 0.0);
default: QL_FAIL("unsupported option type");
}
}
Real sigma2 = sigma()*sigma();
Real h = std::sqrt(k()*k() + 2.0*sigma2);
Real r0 = termStructure()->forwardRate(0.0, 0.0,
Continuous, NoFrequency);
Real b = B(t,s);
Real rho = 2.0*h/(sigma2*(std::exp(h*t) - 1.0));
Real psi = (k() + h)/sigma2;
Real df = 4.0*k()*theta()/sigma2;
Real ncps = 2.0*rho*rho*(r0-phi_(0.0))*std::exp(h*t)/(rho+psi+b);
Real ncpt = 2.0*rho*rho*(r0-phi_(0.0))*std::exp(h*t)/(rho+psi);
NonCentralCumulativeChiSquareDistribution chis(df, ncps);
NonCentralCumulativeChiSquareDistribution chit(df, ncpt);
Real z = std::log(CoxIngersollRoss::A(t,s)/strike)/b;
Real call = discountS*chis(2.0*z*(rho+psi+b)) -
strike*discountT*chit(2.0*z*(rho+psi));
if (type == Option::Call)
return call;
else
return call - discountS + strike*discountT;
}
}