blackkarasinski.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
 
 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 blackkarasinski.hpp
    \brief Black-Karasinski model
*/
 
#ifndef quantlib_black_karasinski_hpp
#define quantlib_black_karasinski_hpp
 
#include <ql/models/shortrate/onefactormodel.hpp>
#include <ql/processes/ornsteinuhlenbeckprocess.hpp>
#include <utility>
 
namespace QuantLib {
 
    //! Standard Black-Karasinski model class.
    /*! This class implements the standard Black-Karasinski model defined by
        \f[
            d\ln r_t = (\theta(t) - \alpha \ln r_t)dt + \sigma dW_t,
        \f]
        where \f$ alpha \f$ and \f$ sigma \f$ are constants.
 
        \ingroup shortrate
    */
    class BlackKarasinski : public OneFactorModel,
                            public TermStructureConsistentModel {
      public:
        BlackKarasinski(const Handle<YieldTermStructure>& termStructure,
                        Real a = 0.1, Real sigma = 0.1);
 
        ext::shared_ptr<ShortRateDynamics> dynamics() const override;
 
        ext::shared_ptr<Lattice> tree(const TimeGrid& grid) const override;
 
      private:
        class Dynamics;
        class Helper;
 
        Real a() const { return a_(0.0); }
        Real sigma() const { return sigma_(0.0); }
 
        Parameter& a_;
        Parameter& sigma_;
        Parameter phi_;
    };
 
    //! Short-rate dynamics in the Black-Karasinski model
    /*! The short-rate is here
        \f[
            r_t = e^{\varphi(t) + x_t}
         \f]
         where \f$ \varphi(t) \f$ is the deterministic time-dependent
         parameter (which can not be determined analytically)
         used for term-structure fitting and \f$ x_t \f$ is the state
         variable following an Ornstein-Uhlenbeck process.
    */
    class BlackKarasinski::Dynamics
        : public BlackKarasinski::ShortRateDynamics {
      public:
        Dynamics(Parameter fitting, Real alpha, Real sigma)
        : ShortRateDynamics(
              ext::shared_ptr<StochasticProcess1D>(new OrnsteinUhlenbeckProcess(alpha, sigma))),
          fitting_(std::move(fitting)) {}
 
        Real variable(Time t, Rate r) const override { return std::log(r) - fitting_(t); }
 
        Real shortRate(Time t, Real x) const override { return std::exp(x + fitting_(t)); }
 
      private:
        Parameter fitting_;
    };
 
}
 
#endif