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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 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.
*/
// ===========================================================================
// NOTE: The following copyright notice applies to the original code,
//
// Copyright (C) 2002 Peter Jäckel "Monte Carlo Methods in Finance".
// All rights reserved.
//
// Permission to use, copy, modify, and distribute this software is freely
// granted, provided that this notice is preserved.
// ===========================================================================
#include <ql/methods/montecarlo/brownianbridge.hpp>
namespace QuantLib {
BrownianBridge::BrownianBridge(Size steps)
: size_(steps), t_(size_), sqrtdt_(size_),
bridgeIndex_(size_), leftIndex_(size_), rightIndex_(size_),
leftWeight_(size_), rightWeight_(size_), stdDev_(size_) {
for (Size i=0; i<size_; ++i)
t_[i] = static_cast<Time>(i+1);
initialize();
}
BrownianBridge::BrownianBridge(const std::vector<Time>& times)
: size_(times.size()), t_(times), sqrtdt_(size_),
bridgeIndex_(size_), leftIndex_(size_), rightIndex_(size_),
leftWeight_(size_), rightWeight_(size_), stdDev_(size_) {
initialize();
}
BrownianBridge::BrownianBridge(const TimeGrid& timeGrid)
: size_(timeGrid.size()-1), t_(size_), sqrtdt_(size_),
bridgeIndex_(size_), leftIndex_(size_), rightIndex_(size_),
leftWeight_(size_), rightWeight_(size_), stdDev_(size_) {
for (Size i=0; i<size_; ++i)
t_[i] = timeGrid[i+1];
initialize();
}
void BrownianBridge::initialize() {
sqrtdt_[0] = std::sqrt(t_[0]);
for (Size i=1; i<size_; ++i)
sqrtdt_[i] = std::sqrt(t_[i]-t_[i-1]);
// map is used to indicate which points are already constructed.
// If map[i] is zero, path point i is yet unconstructed.
// map[i]-1 is the index of the variate that constructs
// the path point # i.
std::vector<Size> map(size_, 0);
// The first point in the construction is the global step.
map[size_-1] = 1;
// The global step is constructed from the first variate.
bridgeIndex_[0] = size_-1;
// The variance of the global step
stdDev_[0] = std::sqrt(t_[size_-1]);
// The global step to the last point in time is special.
leftWeight_[0] = rightWeight_[0] = 0.0;
for (Size j=0, i=1; i<size_; ++i) {
// Find the next unpopulated entry in the map.
while (map[j] != 0U)
++j;
Size k = j;
// Find the next populated entry in the map from there.
while (map[k] == 0U)
++k;
// l-1 is now the index of the point to be constructed next.
Size l = j + ((k-1-j)>>1);
map[l] = i;
// The i-th Gaussian variate will be used to set point l-1.
bridgeIndex_[i] = l;
leftIndex_[i] = j;
rightIndex_[i] = k;
if (j != 0) {
leftWeight_[i]= (t_[k]-t_[l])/(t_[k]-t_[j-1]);
rightWeight_[i] = (t_[l]-t_[j-1])/(t_[k]-t_[j-1]);
stdDev_[i] =
std::sqrt(((t_[l]-t_[j-1])*(t_[k]-t_[l]))
/(t_[k]-t_[j-1]));
} else {
leftWeight_[i] = (t_[k]-t_[l])/t_[k];
rightWeight_[i] = t_[l]/t_[k];
stdDev_[i] = std::sqrt(t_[l]*(t_[k]-t_[l])/t_[k]);
}
j=k+1;
if (j>=size_)
j=0; // wrap around
}
}
}
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