onefactormodel.hpp

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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
 <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.
*/
 
/*! \file onefactormodel.hpp
    \brief Abstract one-factor interest rate model class
*/
 
#ifndef quantlib_one_factor_model_hpp
#define quantlib_one_factor_model_hpp
 
#include <ql/methods/lattices/lattice1d.hpp>
#include <ql/methods/lattices/trinomialtree.hpp>
#include <ql/models/model.hpp>
#include <utility>
 
namespace QuantLib {
    class StochasticProcess1D;
 
    //! Single-factor short-rate model abstract class
    /*! \ingroup shortrate */
    class OneFactorModel : public ShortRateModel {
      public:
        explicit OneFactorModel(Size nArguments);
        ~OneFactorModel() override = default;
 
        class ShortRateDynamics;
        class ShortRateTree;
 
        //! returns the short-rate dynamics
        virtual ext::shared_ptr<ShortRateDynamics> dynamics() const = 0;
 
        //! Return by default a trinomial recombining tree
        ext::shared_ptr<Lattice> tree(const TimeGrid& grid) const override;
    };
 
    //! Base class describing the short-rate dynamics
    class OneFactorModel::ShortRateDynamics {
      public:
        explicit ShortRateDynamics(ext::shared_ptr<StochasticProcess1D> process)
        : process_(std::move(process)) {}
        virtual ~ShortRateDynamics() = default;
 
        //! Compute state variable from short rate
        virtual Real variable(Time t, Rate r) const = 0;
 
        //! Compute short rate from state variable
        virtual Rate shortRate(Time t, Real variable) const = 0;
 
        //! Returns the risk-neutral dynamics of the state variable
        const ext::shared_ptr<StochasticProcess1D>& process() {
            return process_;
        }
      private:
        ext::shared_ptr<StochasticProcess1D> process_;
    };
 
    //! Recombining trinomial tree discretizing the state variable
    class OneFactorModel::ShortRateTree
        : public TreeLattice1D<OneFactorModel::ShortRateTree> {
      public:
        //! Plain tree build-up from short-rate dynamics
        ShortRateTree(const ext::shared_ptr<TrinomialTree>& tree,
                      ext::shared_ptr<ShortRateDynamics> dynamics,
                      const TimeGrid& timeGrid);
        //! Tree build-up + numerical fitting to term-structure
        ShortRateTree(const ext::shared_ptr<TrinomialTree>& tree,
                      ext::shared_ptr<ShortRateDynamics> dynamics,
                      const ext::shared_ptr<TermStructureFittingParameter::NumericalImpl>& phi,
                      const TimeGrid& timeGrid);
 
        Size size(Size i) const {
            return tree_->size(i);
        }
        DiscountFactor discount(Size i, Size index) const {
            Real x = tree_->underlying(i, index);
            Rate r = dynamics_->shortRate(timeGrid()[i], x) +spread_;
            return std::exp(-r*timeGrid().dt(i));
        }
        Real underlying(Size i, Size index) const {
            return tree_->underlying(i, index);
        }
        Size descendant(Size i, Size index, Size branch) const {
            return tree_->descendant(i, index, branch);
        }
        Real probability(Size i, Size index, Size branch) const {
            return tree_->probability(i, index, branch);
        }
        void setSpread(Spread spread)
        {
            spread_=spread;
        }
      private:
        ext::shared_ptr<TrinomialTree> tree_;
        ext::shared_ptr<ShortRateDynamics> dynamics_;
        class Helper;
        Spread spread_;
    };
 
    //! Single-factor affine base class
    /*! Single-factor models with an analytical formula for discount bonds
        should inherit from this class. They must then implement the
        functions \f$ A(t,T) \f$ and \f$ B(t,T) \f$ such that
        \f[
            P(t, T, r_t) = A(t,T)e^{ -B(t,T) r_t}.
        \f]
 
        \ingroup shortrate
    */
    class OneFactorAffineModel : public OneFactorModel,
                                 public AffineModel {
      public:
        explicit OneFactorAffineModel(Size nArguments)
        : OneFactorModel(nArguments) {}
 
        Real discountBond(Time now, Time maturity, Array factors) const override {
            return discountBond(now, maturity, factors[0]);
        }
 
        Real discountBond(Time now, Time maturity, Rate rate) const {
            return A(now, maturity)*std::exp(-B(now, maturity)*rate);
        }
 
        DiscountFactor discount(Time t) const override;
 
      protected:
        virtual Real A(Time t, Time T) const = 0;
        virtual Real B(Time t, Time T) const = 0;
    };
 
}
 
#endif