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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.
*/
#include <ql/methods/lattices/trinomialtree.hpp>
#include <ql/stochasticprocess.hpp>
namespace QuantLib {
TrinomialTree::TrinomialTree(
const ext::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;
QL_REQUIRE(nTimeSteps > 0, "null time steps for trinomial tree");
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);
auto 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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