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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) 2003 Ferdinando Ametrano
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/binomialtree.hpp>
#include <ql/math/distributions/binomialdistribution.hpp>
#include <ql/stochasticprocess.hpp>
namespace QuantLib {
JarrowRudd::JarrowRudd(
const ext::shared_ptr<StochasticProcess1D>& process,
Time end, Size steps, Real)
: EqualProbabilitiesBinomialTree<JarrowRudd>(process, end, steps) {
// drift removed
up_ = process->stdDeviation(0.0, x0_, dt_);
}
CoxRossRubinstein::CoxRossRubinstein(
const ext::shared_ptr<StochasticProcess1D>& process,
Time end, Size steps, Real)
: EqualJumpsBinomialTree<CoxRossRubinstein>(process, end, steps) {
dx_ = process->stdDeviation(0.0, x0_, dt_);
pu_ = 0.5 + 0.5*driftPerStep_/dx_;;
pd_ = 1.0 - pu_;
QL_REQUIRE(pu_<=1.0, "negative probability");
QL_REQUIRE(pu_>=0.0, "negative probability");
}
AdditiveEQPBinomialTree::AdditiveEQPBinomialTree(
const ext::shared_ptr<StochasticProcess1D>& process,
Time end, Size steps, Real)
: EqualProbabilitiesBinomialTree<AdditiveEQPBinomialTree>(process,
end, steps) {
up_ = - 0.5 * driftPerStep_ + 0.5 *
std::sqrt(4.0*process->variance(0.0, x0_, dt_)-
3.0*driftPerStep_*driftPerStep_);
}
Trigeorgis::Trigeorgis(
const ext::shared_ptr<StochasticProcess1D>& process,
Time end, Size steps, Real)
: EqualJumpsBinomialTree<Trigeorgis>(process, end, steps) {
dx_ = std::sqrt(process->variance(0.0, x0_, dt_)+
driftPerStep_*driftPerStep_);
pu_ = 0.5 + 0.5*driftPerStep_/dx_;;
pd_ = 1.0 - pu_;
QL_REQUIRE(pu_<=1.0, "negative probability");
QL_REQUIRE(pu_>=0.0, "negative probability");
}
Tian::Tian(const ext::shared_ptr<StochasticProcess1D>& process,
Time end, Size steps, Real)
: BinomialTree<Tian>(process, end, steps) {
Real q = std::exp(process->variance(0.0, x0_, dt_));
Real r = std::exp(driftPerStep_)*std::sqrt(q);
up_ = 0.5 * r * q * (q + 1 + std::sqrt(q * q + 2 * q - 3));
down_ = 0.5 * r * q * (q + 1 - std::sqrt(q * q + 2 * q - 3));
pu_ = (r - down_) / (up_ - down_);
pd_ = 1.0 - pu_;
// doesn't work
// treeCentering_ = (up_+down_)/2.0;
// up_ = up_-treeCentering_;
QL_REQUIRE(pu_<=1.0, "negative probability");
QL_REQUIRE(pu_>=0.0, "negative probability");
}
LeisenReimer::LeisenReimer(const ext::shared_ptr<StochasticProcess1D>& process,
Time end,
Size steps,
Real strike)
: BinomialTree<LeisenReimer>(process, end, ((steps % 2) != 0U ? steps : (steps + 1))) {
QL_REQUIRE(strike>0.0, "strike must be positive");
Size oddSteps = ((steps % 2) != 0U ? steps : (steps + 1));
Real variance = process->variance(0.0, x0_, end);
Real ermqdt = std::exp(driftPerStep_ + 0.5*variance/oddSteps);
Real d2 = (std::log(x0_/strike) + driftPerStep_*oddSteps ) /
std::sqrt(variance);
pu_ = PeizerPrattMethod2Inversion(d2, oddSteps);
pd_ = 1.0 - pu_;
Real pdash = PeizerPrattMethod2Inversion(d2+std::sqrt(variance),
oddSteps);
up_ = ermqdt * pdash / pu_;
down_ = (ermqdt - pu_ * up_) / (1.0 - pu_);
}
Real Joshi4::computeUpProb(Real k, Real dj) const {
Real alpha = dj/(std::sqrt(8.0));
Real alpha2 = alpha*alpha;
Real alpha3 = alpha*alpha2;
Real alpha5 = alpha3*alpha2;
Real alpha7 = alpha5*alpha2;
Real beta = -0.375*alpha-alpha3;
Real gamma = (5.0/6.0)*alpha5 + (13.0/12.0)*alpha3
+(25.0/128.0)*alpha;
Real delta = -0.1025 *alpha- 0.9285 *alpha3
-1.43 *alpha5 -0.5 *alpha7;
Real p =0.5;
Real rootk = std::sqrt(k);
p+= alpha/rootk;
p+= beta /(k*rootk);
p+= gamma/(k*k*rootk);
// delete next line to get results for j three tree
p+= delta/(k*k*k*rootk);
return p;
}
Joshi4::Joshi4(const ext::shared_ptr<StochasticProcess1D>& process,
Time end,
Size steps,
Real strike)
: BinomialTree<Joshi4>(process, end, (steps % 2) != 0U ? steps : (steps + 1)) {
QL_REQUIRE(strike>0.0, "strike must be positive");
Size oddSteps = (steps % 2) != 0U ? steps : (steps + 1);
Real variance = process->variance(0.0, x0_, end);
Real ermqdt = std::exp(driftPerStep_ + 0.5*variance/oddSteps);
Real d2 = (std::log(x0_/strike) + driftPerStep_*oddSteps ) /
std::sqrt(variance);
pu_ = computeUpProb((oddSteps-1.0)/2.0,d2 );
pd_ = 1.0 - pu_;
Real pdash = computeUpProb((oddSteps-1.0)/2.0,d2+std::sqrt(variance));
up_ = ermqdt * pdash / pu_;
down_ = (ermqdt - pu_ * up_) / (1.0 - pu_);
}
}
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