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| Original file line number | Diff line number | Diff line change |
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| /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ | ||
|
|
||
| /* | ||
| Copyright (C) 2025 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 | ||
| <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/exercise.hpp> | ||
| #include <ql/quotes/simplequote.hpp> | ||
| #include <ql/instruments/basketoption.hpp> | ||
| #include <ql/pricingengines/blackformula.hpp> | ||
| #include <ql/pricingengines/asian/choiasianengine.hpp> | ||
| #include <ql/pricingengines/basket/choibasketengine.hpp> | ||
| #include <ql/termstructures/yield/flatforward.hpp> | ||
| #include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp> | ||
|
|
||
| namespace QuantLib { | ||
|
|
||
| ChoiAsianEngine::ChoiAsianEngine( | ||
| ext::shared_ptr<GeneralizedBlackScholesProcess> process, | ||
| Real lambda, | ||
| Size maxNrIntegrationSteps) | ||
| : process_(std::move(process)), | ||
| lambda_(lambda), | ||
| maxNrIntegrationSteps_(maxNrIntegrationSteps) { | ||
| registerWith(process_); | ||
| } | ||
|
|
||
| void ChoiAsianEngine::calculate() const { | ||
| QL_REQUIRE(arguments_.averageType == Average::Type::Arithmetic, | ||
| "must be Average::Type Arithmetic "); | ||
|
|
||
| QL_REQUIRE(arguments_.exercise->type() == Exercise::European, | ||
| "not a European Option"); | ||
|
|
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| const ext::shared_ptr<PlainVanillaPayoff> payoff = | ||
| ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff); | ||
| QL_REQUIRE(payoff, "non plain vanilla payoff given"); | ||
|
|
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| std::vector<Date> fixingDates = arguments_.fixingDates; | ||
| std::sort(fixingDates.begin(), fixingDates.end()); | ||
|
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| Size futureFixings = fixingDates.size(); | ||
| Size pastFixings = arguments_.pastFixings; | ||
| Real runningAccumulator = arguments_.runningAccumulator; | ||
|
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| const Date exerciseDate = arguments_.exercise->lastDate(); | ||
| const Handle<YieldTermStructure> rTS = process_->riskFreeRate(); | ||
|
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| if ( futureFixings > 0 | ||
| && process_->time(fixingDates.front()) == Time(0)) { | ||
| // push today fixing to past fixings | ||
| fixingDates.erase(fixingDates.begin()); | ||
| futureFixings--; | ||
| pastFixings++; | ||
| runningAccumulator += process_->x0(); | ||
| } | ||
|
|
||
| if (futureFixings == 0) { | ||
| QL_REQUIRE(pastFixings > 0, "no past fixings given"); | ||
| results_.value = (*payoff)(runningAccumulator/pastFixings) | ||
| * rTS->discount(exerciseDate); | ||
|
|
||
| return; | ||
| } | ||
|
|
||
| QL_REQUIRE(fixingDates.back() <= exerciseDate, | ||
| "last fixing date must be before exercise date"); | ||
| QL_REQUIRE(process_->time(fixingDates.front()) >= 0.0, | ||
| "first fixing date is in the past"); | ||
|
|
||
| QL_REQUIRE(std::adjacent_find(fixingDates.begin(), fixingDates.end()) | ||
| == fixingDates.end(), "two fixing dates are the same"); | ||
|
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| const Real accruedAverage = (pastFixings != 0) | ||
| ? runningAccumulator / (pastFixings + futureFixings) | ||
| : 0.0; | ||
|
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| const Real strike = payoff->strike() - accruedAverage; | ||
| QL_REQUIRE(strike >= 0.0, "effective strike should to be positive"); | ||
|
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| const Handle<YieldTermStructure> qTS = process_->dividendYield(); | ||
| const Handle<BlackVolTermStructure> volTS = process_->blackVolatility(); | ||
| const Date volRefDate = volTS->referenceDate(); | ||
| const DayCounter volDc = volTS->dayCounter(); | ||
|
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||
| if (futureFixings > 1) { | ||
| std::vector<Time> fixingTimes(futureFixings), variances(futureFixings); | ||
| for (Size i=0; i < futureFixings; ++i) { | ||
| const Date& fixingDate = fixingDates[i]; | ||
| fixingTimes[i] = volDc.yearFraction(volRefDate, fixingDate); | ||
| variances[i] = process_->blackVolatility()->blackVariance(fixingDate, strike); | ||
| } | ||
|
|
||
| Matrix rho(futureFixings, futureFixings); | ||
| for (Size i=0; i < rho.rows(); ++i) | ||
| for (Size j=i; j < rho.columns(); ++j) | ||
| rho[i][j] = rho[j][i] = | ||
| variances[std::min(i,j)] / std::sqrt(variances[i]*variances[j]); | ||
|
|
||
| const Handle<YieldTermStructure> zeroTS( | ||
| ext::make_shared<FlatForward>(rTS->referenceDate(), 0.0, rTS->dayCounter()) | ||
| ); | ||
|
|
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| std::vector<ext::shared_ptr<GeneralizedBlackScholesProcess> > processes; | ||
| processes.reserve(futureFixings); | ||
| for (Size i=0; i < futureFixings; ++i) { | ||
| const Date& fixingDate = fixingDates[i]; | ||
| const Volatility sig = volTS->blackVol(fixingDate, payoff->strike()) | ||
| * std::sqrt(fixingTimes[i]/fixingTimes.back()); | ||
|
|
||
| processes.emplace_back( | ||
| ext::make_shared<GeneralizedBlackScholesProcess>( | ||
| Handle<Quote>( | ||
| ext::make_shared<SimpleQuote>( | ||
| process_->x0()*qTS->discount(fixingDate)/rTS->discount(fixingDate) | ||
| ) | ||
| ), | ||
| zeroTS, zeroTS, | ||
| Handle<BlackVolTermStructure>( | ||
| ext::make_shared<BlackConstantVol>( | ||
| volRefDate, volTS->calendar(), | ||
| Handle<Quote>(ext::make_shared<SimpleQuote>(sig)), | ||
| volDc | ||
| ) | ||
| ) | ||
| ) | ||
| ); | ||
| } | ||
|
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||
| BasketOption basketOption( | ||
| ext::make_shared<AverageBasketPayoff>( | ||
| ext::make_shared<PlainVanillaPayoff>(payoff->optionType(), strike), | ||
| Array(futureFixings, 1.0/(futureFixings + pastFixings)) | ||
| ), | ||
| ext::make_shared<EuropeanExercise>(fixingDates.back()) | ||
| ); | ||
| basketOption.setPricingEngine( | ||
| ext::make_shared<ChoiBasketEngine>( | ||
| processes, rho, lambda_, maxNrIntegrationSteps_) | ||
| ); | ||
|
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| results_.value = basketOption.NPV() * rTS->discount(exerciseDate); | ||
| } | ||
| else if (futureFixings == 1) { | ||
| results_.value = blackFormula( | ||
| payoff->optionType(), | ||
| strike, | ||
| process_->x0()/(pastFixings + futureFixings) | ||
| *qTS->discount(fixingDates.back())/rTS->discount(fixingDates.back()), | ||
| std::sqrt(volTS->blackVariance(fixingDates.back(), strike)), | ||
| rTS->discount(exerciseDate) | ||
| ); | ||
| } | ||
| } | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,65 @@ | ||
| /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ | ||
|
|
||
| /* | ||
| Copyright (C) 2025 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 | ||
| <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. | ||
| */ | ||
|
|
||
| /*! \file choiasianengine.hpp | ||
| \brief Black Scholes arithmetic Asian option engine | ||
| */ | ||
|
|
||
| #ifndef quantlib_choi_asian_engine_hpp | ||
| #define quantlib_choi_asian_engine_hpp | ||
|
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| #include <ql/pricingengine.hpp> | ||
| #include <ql/instruments/asianoption.hpp> | ||
| #include <ql/processes/blackscholesprocess.hpp> | ||
|
|
||
| namespace QuantLib { | ||
| //! Pricing engine for arithmetic Asian options | ||
| /*! This class replicates an arithmetic Asian option using a basket option. | ||
| The pricing of an arithmetic Asian option is substituted with the pricing | ||
| of a basket option. | ||
| */ | ||
|
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||
| /*! References: | ||
| "Sum of all Black-Scholes-Merton Models: An efficient Pricing Method for | ||
| Spread, Basket and Asian Options", Jaehyuk Choi, 2018 | ||
| https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2913048 | ||
| A Python implementation from the author of the paper is also available | ||
| https://github.com/PyFE/PyFENG | ||
| \ingroup asianengines | ||
| */ | ||
|
|
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| class ChoiAsianEngine : public DiscreteAveragingAsianOption::engine { | ||
| public: | ||
| explicit ChoiAsianEngine( | ||
| ext::shared_ptr<GeneralizedBlackScholesProcess> p, | ||
| Real lambda = 15, | ||
| Size maxNrIntegrationSteps = 2 << 21); | ||
|
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| void calculate() const override; | ||
|
|
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| private: | ||
| const ext::shared_ptr<GeneralizedBlackScholesProcess> process_; | ||
| const Real lambda_; | ||
| const Size maxNrIntegrationSteps_; | ||
| }; | ||
| } | ||
|
|
||
| #endif |
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