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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Klaus Spanderen
Copyright (C) 2010 Kakhkhor Abdijalilov
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.
*/
/*! \file lsmbasissystem.cpp
\brief utility classes for longstaff schwartz early exercise Monte Carlo
*/
#include <ql/math/integrals/gaussianquadratures.hpp>
#include <ql/methods/montecarlo/lsmbasissystem.hpp>
#include <numeric>
#include <set>
#include <utility>
namespace QuantLib {
namespace {
// makes typing a little easier
typedef std::vector<std::function<Real(Real)> > VF_R;
typedef std::vector<std::function<Real(Array)> > VF_A;
typedef std::vector<std::vector<Size> > VV;
// pow(x, order)
class MonomialFct {
public:
explicit MonomialFct(Size order): order_(order) {}
Real operator()(const Real x) const {
Real ret = 1.0;
for(Size i=0; i<order_; ++i)
ret *= x;
return ret;
}
private:
const Size order_;
};
/* multiplies [Real -> Real] functors
to create [Array -> Real] functor */
class MultiDimFct {
public:
explicit MultiDimFct(VF_R b) : b_(std::move(b)) {
QL_REQUIRE(!b_.empty(), "zero size basis");
}
Real operator()(const Array& a) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(b_.size()==a.size(), "wrong argument size");
#endif
Real ret = b_[0](a[0]);
for(Size i=1; i<b_.size(); ++i)
ret *= b_[i](a[i]);
return ret;
}
private:
const VF_R b_;
};
// check size and order of tuples
void check_tuples(const VV& v, Size dim, Size order) {
for (const auto& i : v) {
QL_REQUIRE(dim == i.size(), "wrong tuple size");
QL_REQUIRE(order == std::accumulate(i.begin(), i.end(), 0UL), "wrong tuple order");
}
}
// build order N+1 tuples from order N tuples
VV next_order_tuples(const VV& v) {
const Size order = std::accumulate(v[0].begin(), v[0].end(), 0UL);
const Size dim = v[0].size();
check_tuples(v, dim, order);
// the set of unique tuples
std::set<std::vector<Size> > tuples;
std::vector<Size> x;
for(Size i=0; i<dim; ++i) {
// increase i-th value in every tuple by 1
for (const auto& j : v) {
x = j;
x[i] += 1;
tuples.insert(x);
}
}
VV ret(tuples.begin(), tuples.end());
return ret;
}
}
// LsmBasisSystem static methods
VF_R LsmBasisSystem::pathBasisSystem(Size order, PolynomialType type) {
VF_R ret(order+1);
for (Size i=0; i<=order; ++i) {
switch (type) {
case Monomial:
ret[i] = MonomialFct(i);
break;
case Laguerre:
{
GaussLaguerrePolynomial p;
ret[i] = [=](Real x){ return p.weightedValue(i, x); };
}
break;
case Hermite:
{
GaussHermitePolynomial p;
ret[i] = [=](Real x){ return p.weightedValue(i, x); };
}
break;
case Hyperbolic:
{
GaussHyperbolicPolynomial p;
ret[i] = [=](Real x){ return p.weightedValue(i, x); };
}
break;
case Legendre:
{
GaussLegendrePolynomial p;
ret[i] = [=](Real x){ return p.weightedValue(i, x); };
}
break;
case Chebyshev:
{
GaussChebyshevPolynomial p;
ret[i] = [=](Real x){ return p.weightedValue(i, x); };
}
break;
case Chebyshev2nd:
{
GaussChebyshev2ndPolynomial p;
ret[i] = [=](Real x){ return p.weightedValue(i, x); };
}
break;
default:
QL_FAIL("unknown regression type");
}
}
return ret;
}
VF_A LsmBasisSystem::multiPathBasisSystem(Size dim, Size order,
PolynomialType type) {
QL_REQUIRE(dim>0, "zero dimension");
// get single factor basis
VF_R pathBasis = pathBasisSystem(order, type);
VF_A ret;
// 0-th order term
VF_R term(dim, pathBasis[0]);
ret.emplace_back(MultiDimFct(term));
// start with all 0 tuple
VV tuples(1, std::vector<Size>(dim));
// add multi-factor terms
for(Size i=1; i<=order; ++i) {
tuples = next_order_tuples(tuples);
// now we have all tuples of order i
// for each tuple add the corresponding term
for (auto& tuple : tuples) {
for(Size k=0; k<dim; ++k)
term[k] = pathBasis[tuple[k]];
ret.emplace_back(MultiDimFct(term));
}
}
return ret;
}
}
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