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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.
*/
/*! \file singlefactorbsmbasketengine.cpp
*/
#include <ql/exercise.hpp>
#include <ql/math/functional.hpp>
#include <ql/math/solvers1d/brent.hpp>
#include <ql/math/solvers1d/newton.hpp>
#include <ql/math/solvers1d/ridder.hpp>
#include <ql/math/solvers1d/halley.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/pricingengines/basket/vectorbsmprocessextractor.hpp>
#include <ql/pricingengines/basket/singlefactorbsmbasketengine.hpp>
namespace QuantLib {
namespace detail {
SumExponentialsRootSolver::SumExponentialsRootSolver(
Array a, Array sig, Real K)
: a_(std::move(a)), sig_(std::move(sig)), K_(K) {
QL_REQUIRE(a_.size() == sig_.size(),
"Arrays must have the same size");
}
Real SumExponentialsRootSolver::operator()(Real x) const {
++fCtr_;
Real s = 0.0;
for (Size i=0; i < a_.size(); ++i)
s += a_[i]*std::exp(sig_[i]*x);
return s - K_;
}
Real SumExponentialsRootSolver::derivative(Real x) const {
++fPrimeCtr_;
Real s = 0.0;
for (Size i=0; i < a_.size(); ++i)
s += a_[i]*sig_[i]*std::exp(sig_[i]*x);
return s;
}
Real SumExponentialsRootSolver::secondDerivative(Real x) const {
++fDoublePrimeCtr_;
Real s = 0.0;
for (Size i=0; i < a_.size(); ++i)
s += a_[i]*squared(sig_[i])*std::exp(sig_[i]*x);
return s;
}
Size SumExponentialsRootSolver::getFCtr() const {
return fCtr_;
}
Size SumExponentialsRootSolver::getDerivativeCtr() const {
return fPrimeCtr_;
}
Size SumExponentialsRootSolver::getSecondDerivativeCtr() const {
return fDoublePrimeCtr_;
}
Real SumExponentialsRootSolver::getRoot(Real xTol, Strategy strategy) const {
const Array attr = a_*sig_;
QL_REQUIRE(
std::all_of(
attr.begin(), attr.end(),
[](Real x) -> bool { return x >= 0.0; }
),
"a*sig should not be negative"
);
const bool logProb =
std::all_of(
a_.begin(), a_.end(),
[](Real x) -> bool { return x > 0;}
);
QL_REQUIRE(K_ > 0 || !logProb,
"non-positive strikes only allowed for spread options");
// linear approximation
const Real denom = std::accumulate(attr.begin(), attr.end(), Real(0.0));
const Real xInit = (std::abs(denom) > 1000*QL_EPSILON)
? std::min(10.0, std::max(-10.0,
(K_ - std::accumulate(a_.begin(), a_.end(), Real(0.0)))/denom)
)
: Real(0.0);
switch(strategy) {
case Brent:
return QuantLib::Brent().solve(*this, xTol, xInit, 1.0);
case Newton:
return QuantLib::Newton().solve(*this, xTol, xInit, 1.0);
case Ridder:
return QuantLib::Ridder().solve(*this, xTol, xInit, 1.0);
case Halley:
return QuantLib::Halley().solve(*this, xTol, xInit, 1.0);
default:
QL_FAIL("unknown strategy type");
}
}
}
SingleFactorBsmBasketEngine::SingleFactorBsmBasketEngine(
std::vector<ext::shared_ptr<GeneralizedBlackScholesProcess> > p,
Real xTol)
: xTol_(xTol),
n_(p.size()), processes_(std::move(p)) {
std::for_each(processes_.begin(), processes_.end(),
[this](const auto& p) { registerWith(p); });
}
void SingleFactorBsmBasketEngine::calculate() const {
const ext::shared_ptr<AverageBasketPayoff> avgPayoff =
ext::dynamic_pointer_cast<AverageBasketPayoff>(arguments_.payoff);
QL_REQUIRE(avgPayoff, "average basket payoff expected");
const ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(avgPayoff->basePayoff());
QL_REQUIRE(payoff, "non-plain vanilla payoff given");
const Real strike = payoff->strike();
const Array weights = avgPayoff->weights();
QL_REQUIRE(n_ == weights.size(),
"wrong number of weights arguments in payoff");
const ext::shared_ptr<EuropeanExercise> exercise =
ext::dynamic_pointer_cast<EuropeanExercise>(arguments_.exercise);
QL_REQUIRE(exercise, "not an European exercise");
const Date maturityDate = exercise->lastDate();
const detail::VectorBsmProcessExtractor pExtractor(processes_);
const Array s = pExtractor.getSpot();
const Array dq = pExtractor.getDividendYieldDf(maturityDate);
const DiscountFactor dr0 = pExtractor.getInterestRateDf(maturityDate);
const Array stdDev = pExtractor.getBlackStdDev(maturityDate);
const Array v = stdDev*stdDev;
const Array fwdBasket = weights * s * dq /dr0;
// first check if all vols are zero -> intrinsic case
if (std::all_of(
stdDev.begin(), stdDev.end(),
[](Real x) -> bool { return close_enough(x, 0.0); }
)) {
results_.value = dr0*payoff->operator()(
std::accumulate(fwdBasket.begin(), fwdBasket.end(), Real(0.0)));
}
else {
const Real d = -detail::SumExponentialsRootSolver(
fwdBasket*Exp(-0.5*v), stdDev, strike)
.getRoot(xTol_, detail::SumExponentialsRootSolver::Brent);
const CumulativeNormalDistribution N;
const Real cp = (payoff->optionType() == Option::Call) ? 1.0 : -1.0;
results_.value = cp * dr0 *
std::inner_product(
fwdBasket.begin(), fwdBasket.end(), stdDev.begin(),
Real(-strike*N(cp*d)),
std::plus<>(),
[d, cp, &N](Real x, Real y) -> Real { return x*N(cp*(d+y)); }
);
results_.additionalResults["d"] = d;
}
}
}
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