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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2024 Klaus Spanderen
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/exercise.hpp>
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/math/matrixutilities/getcovariance.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/matrixutilities/symmetricschurdecomposition.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/predefined1dmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmwienerop.hpp>
#include <ql/methods/finitedifferences/solvers/fdmndimsolver.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/pricingengines/basket/fdndimblackscholesvanillaengine.hpp>
#include <ql/pricingengines/basket/vectorbsmprocessextractor.hpp>
#include <boost/preprocessor/iteration/local.hpp>
#include <utility>
namespace QuantLib {
namespace detail {
class FdmPCABasketInnerValue: public FdmInnerValueCalculator {
public:
FdmPCABasketInnerValue(
ext::shared_ptr<BasketPayoff> payoff,
ext::shared_ptr<FdmMesher> mesher,
Array logS0, const Array& vols,
std::vector<ext::shared_ptr<YieldTermStructure>> qTS,
ext::shared_ptr<YieldTermStructure> rTS,
Matrix Q, Array l)
: n_(logS0.size()),
payoff_(std::move(payoff)),
mesher_(std::move(mesher)),
logS0_(std::move(logS0)), v_(vols*vols),
qTS_(std::move(qTS)),
rTS_(std::move(rTS)),
Q_(std::move(Q)), l_(std::move(l)),
cachedT_(Null<Real>()),
qf_(n_) { }
Real innerValue(const FdmLinearOpIterator& iter, Time t) override {
if (!close_enough(t, cachedT_)) {
rf_ = rTS_->discount(t);
for (Size i=0; i < n_; ++i)
qf_[i] = qTS_[i]->discount(t);
}
Array x(n_);
for (Size i=0; i < n_; ++i)
x[i] = mesher_->location(iter, i);
const Array S = Exp(Q_*x - 0.5*v_*t + logS0_)*qf_/rf_;
return (*payoff_)(S);
}
Real avgInnerValue(const FdmLinearOpIterator& iter, Time t) override {
return innerValue(iter, t);
}
private:
const Size n_;
const ext::shared_ptr<BasketPayoff> payoff_;
const ext::shared_ptr<FdmMesher> mesher_;
const Array logS0_, v_;
const std::vector<ext::shared_ptr<YieldTermStructure>> qTS_;
const ext::shared_ptr<YieldTermStructure> rTS_;
const Matrix Q_;
const Array l_;
Time cachedT_;
Array qf_;
DiscountFactor rf_;
};
}
FdndimBlackScholesVanillaEngine::FdndimBlackScholesVanillaEngine(
std::vector<ext::shared_ptr<GeneralizedBlackScholesProcess> > processes,
Matrix rho,
std::vector<Size> xGrids,
Size tGrid, Size dampingSteps,
const FdmSchemeDesc& schemeDesc)
: processes_(std::move(processes)),
rho_(std::move(rho)),
xGrids_(std::move(xGrids)),
tGrid_(tGrid),
dampingSteps_(dampingSteps),
schemeDesc_(schemeDesc) {
QL_REQUIRE(!processes_.empty(), "no Black-Scholes process is given.");
QL_REQUIRE(rho_.size1() == rho_.size2()
&& rho_.size1() == processes_.size(),
"correlation matrix has the wrong size.");
QL_REQUIRE(xGrids_.size() == 1 || xGrids_.size() == processes_.size(),
"wrong number of xGrids is given.");
std::for_each(processes_.begin(), processes_.end(),
[this](const auto& p) { registerWith(p); });
}
FdndimBlackScholesVanillaEngine::FdndimBlackScholesVanillaEngine(
std::vector<ext::shared_ptr<GeneralizedBlackScholesProcess> > processes,
Matrix rho, Size xGrid, Size tGrid, Size dampingSteps,
const FdmSchemeDesc& schemeDesc)
: FdndimBlackScholesVanillaEngine(
std::move(processes), std::move(rho), std::vector<Size>(1, xGrid), tGrid, dampingSteps, schemeDesc)
{}
void FdndimBlackScholesVanillaEngine::calculate() const {
#ifndef PDE_MAX_SUPPORTED_DIM
#define PDE_MAX_SUPPORTED_DIM 4
#endif
QL_REQUIRE(processes_.size() <= PDE_MAX_SUPPORTED_DIM,
"This engine does not support " << processes_.size() << " underlyings. "
<< "Max number of underlyings is " << PDE_MAX_SUPPORTED_DIM << ". "
<< "Please change preprocessor constant PDE_MAX_SUPPORTED_DIM and recompile "
<< "if a larger number of underlyings is needed.");
const Date maturityDate = arguments_.exercise->lastDate();
const Time maturity = processes_[0]->time(maturityDate);
const Real sqrtT = std::sqrt(maturity);
const detail::VectorBsmProcessExtractor pExtractor(processes_);
const Array s = pExtractor.getSpot();
const Array dq = pExtractor.getDividendYieldDf(maturityDate);
const Array stdDev = Sqrt(pExtractor.getBlackVariance(maturityDate));
const Array vols = stdDev / sqrtT;
const SymmetricSchurDecomposition schur(
getCovariance(vols.begin(), vols.end(), rho_));
const Matrix& Q = schur.eigenvectors();
const Array& l = schur.eigenvalues();
const Real eps = 1e-4;
std::vector<ext::shared_ptr<Fdm1dMesher> > meshers;
for (Size i=0; i < processes_.size(); ++i) {
const Size xGrid = (xGrids_.size() > 1)
? xGrids_[i]
: std::max(Size(4), Size(xGrids_[0]*std::pow(l[i]/l[0], 0.1)));
QL_REQUIRE(xGrid >= 4, "minimum grid size is four");
const Real xStepStize = (1.0-2*eps)/(xGrid-1);
std::vector<Real> x(xGrid);
for (Size j=0; j < xGrid; ++j)
x[j] = 1.3*std::sqrt(l[i])*sqrtT
*InverseCumulativeNormal()(eps + j*xStepStize);
meshers.emplace_back(ext::make_shared<Predefined1dMesher>(x));
}
const ext::shared_ptr<FdmMesherComposite> mesher =
ext::make_shared<FdmMesherComposite>(meshers);
const ext::shared_ptr<BasketPayoff> payoff
= ext::dynamic_pointer_cast<BasketPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "basket payoff expected");
const ext::shared_ptr<YieldTermStructure> rTS =
processes_[0]->riskFreeRate().currentLink();
std::vector<ext::shared_ptr<YieldTermStructure>> qTS(processes_.size());
for (Size i=0; i < processes_.size(); ++i)
qTS[i] = processes_[i]->dividendYield().currentLink();
const ext::shared_ptr<FdmInnerValueCalculator> calculator =
ext::make_shared<detail::FdmPCABasketInnerValue>(
payoff, mesher,
Log(s), stdDev/sqrtT,
qTS, rTS,
Q, l
);
const ext::shared_ptr<FdmStepConditionComposite> conditions
= FdmStepConditionComposite::vanillaComposite(
DividendSchedule(), arguments_.exercise,
mesher, calculator,
rTS->referenceDate(), rTS->dayCounter());
const FdmBoundaryConditionSet boundaries;
const FdmSolverDesc solverDesc
= { mesher, boundaries, conditions, calculator,
maturity, tGrid_, dampingSteps_ };
const bool isEuropean =
ext::dynamic_pointer_cast<EuropeanExercise>(arguments_.exercise) != nullptr;
const ext::shared_ptr<FdmWienerOp> op =
ext::make_shared<FdmWienerOp>(
mesher,
(isEuropean)? ext::shared_ptr<YieldTermStructure>() : rTS,
l);
switch(processes_.size()) {
#define BOOST_PP_LOCAL_MACRO(n) \
case n : \
results_.value = ext::make_shared<FdmNdimSolver<n>>( \
solverDesc, schemeDesc_, op)->interpolateAt( \
std::vector<Real>(processes_.size(), 0.0)); \
break;
#define BOOST_PP_LOCAL_LIMITS (1, PDE_MAX_SUPPORTED_DIM)
#include BOOST_PP_LOCAL_ITERATE()
default:
QL_FAIL("Not implemented for " << processes_.size() << " processes");
}
if (isEuropean)
results_.value *= pExtractor.getInterestRateDf(maturityDate);
}
}
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