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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
Copyright (C) 2005 StatPro Italia srl
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.
*/
/*! \file twofactormodel.hpp
\brief Abstract two-factor interest rate model class
*/
#ifndef quantlib_two_factor_model_hpp
#define quantlib_two_factor_model_hpp
#include <ql/methods/lattices/lattice2d.hpp>
#include <ql/models/model.hpp>
#include <utility>
namespace QuantLib {
class StochasticProcess1D;
class StochasticProcess;
//! Abstract base-class for two-factor models
/*! \ingroup shortrate */
class TwoFactorModel : public ShortRateModel {
public:
explicit TwoFactorModel(Size nParams);
class ShortRateDynamics;
class ShortRateTree;
//! Returns the short-rate dynamics
virtual ext::shared_ptr<ShortRateDynamics> dynamics() const = 0;
//! Returns a two-dimensional trinomial tree
ext::shared_ptr<Lattice> tree(const TimeGrid& grid) const override;
};
//! Class describing the dynamics of the two state variables
/*! We assume here that the short-rate is a function of two state
variables x and y.
\f[
r_t = f(t, x_t, y_t)
\f]
of two state variables \f$ x_t \f$ and \f$ y_t \f$. These stochastic
processes satisfy
\f[
x_t = \mu_x(t, x_t)dt + \sigma_x(t, x_t) dW_t^x
\f]
and
\f[
y_t = \mu_y(t,y_t)dt + \sigma_y(t, y_t) dW_t^y
\f]
where \f$ W^x \f$ and \f$ W^y \f$ are two brownian motions
satisfying
\f[
dW^x_t dW^y_t = \rho dt
\f].
*/
class TwoFactorModel::ShortRateDynamics {
public:
ShortRateDynamics(ext::shared_ptr<StochasticProcess1D> xProcess,
ext::shared_ptr<StochasticProcess1D> yProcess,
Real correlation)
: xProcess_(std::move(xProcess)), yProcess_(std::move(yProcess)),
correlation_(correlation) {}
virtual ~ShortRateDynamics() = default;
virtual Rate shortRate(Time t, Real x, Real y) const = 0;
//! Risk-neutral dynamics of the first state variable x
const ext::shared_ptr<StochasticProcess1D>& xProcess() const {
return xProcess_;
}
//! Risk-neutral dynamics of the second state variable y
const ext::shared_ptr<StochasticProcess1D>& yProcess() const {
return yProcess_;
}
//! Correlation \f$ \rho \f$ between the two brownian motions.
Real correlation() const {
return correlation_;
}
//! Joint process of the two variables
ext::shared_ptr<StochasticProcess> process() const;
private:
ext::shared_ptr<StochasticProcess1D> xProcess_, yProcess_;
Real correlation_;
};
//! Recombining two-dimensional tree discretizing the state variable
class TwoFactorModel::ShortRateTree
: public TreeLattice2D<TwoFactorModel::ShortRateTree,TrinomialTree> {
public:
//! Plain tree build-up from short-rate dynamics
ShortRateTree(const ext::shared_ptr<TrinomialTree>& tree1,
const ext::shared_ptr<TrinomialTree>& tree2,
const ext::shared_ptr<ShortRateDynamics>& dynamics);
DiscountFactor discount(Size i, Size index) const {
Size modulo = tree1_->size(i);
Size index1 = index % modulo;
Size index2 = index / modulo;
Real x = tree1_->underlying(i, index1);
Real y = tree2_->underlying(i, index2);
Rate r = dynamics_->shortRate(timeGrid()[i], x, y);
return std::exp(-r*timeGrid().dt(i));
}
private:
ext::shared_ptr<ShortRateDynamics> dynamics_;
};
}
#endif
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