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trinomialtree.cpp

/* -*- 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.
*/

#include <ql/methods/lattices/trinomialtree.hpp>
#include <ql/stochasticprocess.hpp>

namespace QuantLib {

    TrinomialTree::TrinomialTree(
                        const boost::shared_ptr<StochasticProcess1D>& process,
                        const TimeGrid& timeGrid,
                        bool isPositive)
    : Tree<TrinomialTree>(timeGrid.size()), dx_(1, 0.0), timeGrid_(timeGrid) {
        x0_ = process->x0();

        Size nTimeSteps = timeGrid.size() - 1;
        Integer jMin = 0;
        Integer jMax = 0;

        for (Size i=0; i<nTimeSteps; i++) {
            Time t = timeGrid[i];
            Time dt = timeGrid.dt(i);

            //Variance must be independent of x
            Real v2 = process->variance(t, 0.0, dt);
            Volatility v = std::sqrt(v2);
            dx_.push_back(v*std::sqrt(3.0));

            Branching branching;
            for (Integer j=jMin; j<=jMax; j++) {
                Real x = x0_ + j*dx_[i];
                Real m = process->expectation(t, x, dt);
                Integer temp = Integer(std::floor((m-x0_)/dx_[i+1] + 0.5));

                if (isPositive) {
                    while (x0_+(temp-1)*dx_[i+1]<=0) {
                        temp++;
                    }
                }

                Real e = m - (x0_ + temp*dx_[i+1]);
                Real e2 = e*e;
                Real e3 = e*std::sqrt(3.0);

                Real p1 = (1.0 + e2/v2 - e3/v)/6.0;
                Real p2 = (2.0 - e2/v2)/3.0;
                Real p3 = (1.0 + e2/v2 + e3/v)/6.0;

                branching.add(temp, p1, p2, p3);
            }
            branchings_.push_back(branching);

            jMin = branching.jMin();
            jMax = branching.jMax();
        }
    }

}


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