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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Mark Joshi
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/models/marketmodels/evolvers/volprocesses/squarerootandersen.hpp>
#include <ql/errors.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
namespace
QuantLib
{
SquareRootAndersen::SquareRootAndersen(Real meanLevel,
Real reversionSpeed,
Real volVar,
Real v0,
const std::vector<Real>& evolutionTimes,
Size numberSubSteps,
Real w1,
Real w2,
Real cutPoint )
:
theta_(meanLevel),
k_(reversionSpeed),
epsilon_(volVar),
v0_(v0),
numberSubSteps_(numberSubSteps),
dt_(evolutionTimes.size()*numberSubSteps),
eMinuskDt_(evolutionTimes.size()*numberSubSteps),
w1_(w1),
w2_(w2),
PsiC_(cutPoint),
vPath_(evolutionTimes.size()*numberSubSteps+1),
state_(1)
{
Size j=0;
for (; j < numberSubSteps_; ++j)
dt_[j] = evolutionTimes[0]/numberSubSteps_;
for (Size i=1; i < evolutionTimes.size(); ++i)
{
Real dt = (evolutionTimes[i] - evolutionTimes[i-1])/numberSubSteps_;
Real ekdt = std::exp(-k_*dt);
QL_REQUIRE(dt >0.0, "Steps must be of positive size.");
for (Size k=0; k < numberSubSteps_; ++k)
{
dt_[j] = dt;
eMinuskDt_[j] = ekdt;
++j;
}
}
vPath_[0] = v0_;
}
Size SquareRootAndersen::variatesPerStep()
{
return numberSubSteps_;
}
Size SquareRootAndersen::numberSteps()
{
return dt_.size()*numberSubSteps_;
}
void SquareRootAndersen::nextPath()
{
v_=v0_;
currentStep_=0;
subStep_=0;
}
void SquareRootAndersen::DoOneSubStep(Real& vt, Real z, Size j)
{
Real eminuskT = eMinuskDt_[j];
Real m = theta_+(vt-theta_)*eminuskT;
Real s2= vt*epsilon_*epsilon_*eminuskT*(1-eminuskT)/k_
+ theta_*epsilon_*epsilon_*(1- eminuskT)*(1- eminuskT)/(2*k_);
Real s = std::sqrt(s2);
Real psi = s*s/(m*m);
if (psi<= PsiC_)
{
Real psiinv = 1.0/psi;
Real b2 = 2.0*psiinv -1+std::sqrt(2*psiinv*(2*psiinv-1.0));
Real b = std::sqrt(b2);
Real a= m/(1+b2);
vt= a*(b+z)*(b+z);
}
else
{
Real p = (psi-1.0)/(psi+1.0);
Real beta = (1.0-p)/m;
Real u = CumulativeNormalDistribution()(z);
if (u < p)
{
vt=0;
return;
}
vt = std::log((1.0-p)/(1.0-u))/beta;
}
}
Real SquareRootAndersen::nextstep(const std::vector<Real>& variates)
{
for (Size j=0; j < numberSubSteps_; ++j)
{
DoOneSubStep(v_, variates[j], subStep_);
++subStep_;
vPath_[subStep_] = v_;
}
++currentStep_;
return 1.0; // no importance sampling here
}
Real SquareRootAndersen::stepSd() const
{
QL_REQUIRE(currentStep_>0, "nextStep must be called before stepSd");
Real stepVariance =0.0;
Size lastStepStart = (currentStep_-1)*numberSubSteps_;
for (Size k=0; k < numberSubSteps_; ++k)
stepVariance += w1_*vPath_[k+lastStepStart]+w2_*vPath_[k+lastStepStart+1];
stepVariance /= numberSubSteps_;
return std::sqrt(stepVariance);
}
const std::vector<Real>& SquareRootAndersen::stateVariables() const
{
state_[0] = v_;
return state_;
}
Size SquareRootAndersen::numberStateVariables() const
{
return 1;
}
}
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