bsmlattice.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 bsmlattice.hpp
    \brief Binomial trees under the BSM model
*/
 
#ifndef quantlib_bsm_lattice_hpp
#define quantlib_bsm_lattice_hpp
 
#include <ql/methods/lattices/binomialtree.hpp>
#include <ql/methods/lattices/lattice1d.hpp>
 
namespace QuantLib {
 
    //! Simple binomial lattice approximating the Black-Scholes model
    /*! \ingroup lattices */
    template <class T>
    class BlackScholesLattice : public TreeLattice1D<BlackScholesLattice<T> > {
      public:
        BlackScholesLattice(const ext::shared_ptr<T>& tree,
                            Rate riskFreeRate,
                            Time end,
                            Size steps);
 
        Rate riskFreeRate() const { return riskFreeRate_; }
        Time dt() const { return dt_; }
        Size size(Size i) const { return tree_->size(i); }
        DiscountFactor discount(Size,
                                Size) const { return discount_; }
 
        void stepback(Size i, const Array& values, Array& newValues) const;
 
        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);
        }
      protected:
        ext::shared_ptr<T> tree_;
        Rate riskFreeRate_;
        Time dt_;
        DiscountFactor discount_;
        Real pd_, pu_;
    };
 
 
    // template definitions
 
    template <class T>
    BlackScholesLattice<T>::BlackScholesLattice(
                                            const ext::shared_ptr<T>& tree,
                                            Rate riskFreeRate,
                                            Time end,
                                            Size steps)
    : TreeLattice1D<BlackScholesLattice<T> >(TimeGrid(end, steps), 2),
      tree_(tree), riskFreeRate_(riskFreeRate), dt_(end/steps),
      discount_(std::exp(-riskFreeRate*(dt_))),
      pd_(tree->probability(0, 0, 0)), pu_(tree->probability(0, 0, 1)) {}
 
    template <class T>
    void BlackScholesLattice<T>::stepback(Size i, const Array& values,
                                          Array& newValues) const {
        for (Size j=0; j<size(i); j++)
            newValues[j] = (pd_*values[j] + pu_*values[j+1])*discount_;
    }
 
}
 
 
#endif