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Turnbull-Wakeman engine for discrete Asian options
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| /* | ||
| Copyright (C) 2021 Skandinaviska Enskilda Banken AB (publ) | ||
| 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 | ||
| <[email protected]>. 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. | ||
| */ | ||
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| #include <ql/exercise.hpp> | ||
| #include <ql/pricingengines/asian/turnbullwakemanasianengine.hpp> | ||
| #include <ql/pricingengines/blackformula.hpp> | ||
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| using namespace QuantLib; | ||
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| void TurnbullWakemanAsianEngine::calculate() const { | ||
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| // Enforce a few required things | ||
| QL_REQUIRE(arguments_.exercise->type() == Exercise::European, "not a European Option"); | ||
| QL_REQUIRE(arguments_.averageType == Average::Type::Arithmetic, | ||
| "must be Arithmetic Average::Type"); | ||
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| // Calculate the accrued portion | ||
| Size pastFixings = arguments_.pastFixings; | ||
| Size futureFixings = arguments_.fixingDates.size(); | ||
| Real accruedAverage = 0; | ||
| if (pastFixings != 0) { | ||
| accruedAverage = arguments_.runningAccumulator / (pastFixings + futureFixings); | ||
| } | ||
| results_.additionalResults["accrued"] = accruedAverage; | ||
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| Real discount = process_->riskFreeRate()->discount(arguments_.exercise->lastDate()); | ||
| results_.additionalResults["discount"] = discount; | ||
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| ext::shared_ptr<PlainVanillaPayoff> payoff = | ||
| ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff); | ||
| QL_REQUIRE(payoff, "non-plain payoff given"); | ||
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| // We will read the volatility off the surface at the effective strike | ||
| Real effectiveStrike = payoff->strike() - accruedAverage; | ||
| results_.additionalResults["strike"] = payoff->strike(); | ||
| results_.additionalResults["effective_strike"] = effectiveStrike; | ||
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| // If the effective strike is negative, exercise resp. permanent OTM is guaranteed and the | ||
| // valuation is made easy | ||
| Size m = futureFixings + pastFixings; | ||
| if (effectiveStrike <= 0.0) { | ||
| // For a reference, see "Option Pricing Formulas", Haug, 2nd ed, p. 193 | ||
| if (payoff->optionType() == Option::Type::Call) { | ||
| Real spot = process_->stateVariable()->value(); | ||
| Real S_A_hat = accruedAverage; | ||
| for (const auto& fd : arguments_.fixingDates) { | ||
| S_A_hat += (spot * process_->dividendYield()->discount(fd) / | ||
| process_->riskFreeRate()->discount(fd)) / | ||
| m; | ||
| } | ||
| results_.value = discount * (S_A_hat - payoff->strike()); | ||
| } else if (payoff->optionType() == Option::Type::Put) { | ||
| results_.value = 0; | ||
| } | ||
| return; | ||
| } | ||
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| // We should only get this far when the effectiveStrike > 0 but will check anyway | ||
| QL_REQUIRE(effectiveStrike > 0.0, "expected effectiveStrike to be positive"); | ||
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| // Expected value of the non-accrued portion of the average prices | ||
| // In general, m will equal n below if there is no accrued. If accrued, m > n. | ||
| Real EA = 0.0; | ||
| std::vector<Real> forwards; | ||
| std::vector<Time> times; | ||
| std::vector<Real> spotVars; | ||
| std::vector<Real> spotVolsVec; // additional results only | ||
| Real spot = process_->stateVariable()->value(); | ||
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| for (const auto& fd : arguments_.fixingDates) { | ||
| DiscountFactor dividendDiscount = process_->dividendYield()->discount(fd); | ||
| DiscountFactor riskFreeDiscountForFwdEstimation = process_->riskFreeRate()->discount(fd); | ||
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| forwards.push_back(spot * dividendDiscount / riskFreeDiscountForFwdEstimation); | ||
| times.push_back(process_->blackVolatility()->timeFromReference(fd)); | ||
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| spotVars.push_back( | ||
| process_->blackVolatility()->blackVariance(times.back(), effectiveStrike)); | ||
| spotVolsVec.push_back(std::sqrt(spotVars.back() / times.back())); | ||
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| EA += forwards.back(); | ||
| } | ||
| EA /= m; | ||
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| // Expected value of A^2. | ||
| Real EA2 = 0.0; | ||
| Size n = forwards.size(); | ||
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| for (Size i = 0; i < n; ++i) { | ||
| EA2 += forwards[i] * forwards[i] * exp(spotVars[i]); | ||
| for (Size j = 0; j < i; ++j) { | ||
| EA2 += 2 * forwards[i] * forwards[j] * exp(spotVars[j]); | ||
| } | ||
| } | ||
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| EA2 /= m * m; | ||
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| // Calculate value | ||
| Real tn = times.back(); | ||
| Real sigma = sqrt(log(EA2 / (EA * EA)) / tn); | ||
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| // Populate results | ||
| results_.value = | ||
| blackFormula(payoff->optionType(), effectiveStrike, EA, sigma * sqrt(tn), discount); | ||
| results_.additionalResults["forward"] = EA; | ||
| results_.additionalResults["exp_A_2"] = EA2; | ||
| results_.additionalResults["tte"] = tn; | ||
| results_.additionalResults["sigma"] = sigma; | ||
| results_.additionalResults["times"] = times; | ||
| results_.additionalResults["spotVols"] = spotVolsVec; | ||
| results_.additionalResults["forwards"] = forwards; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,62 @@ | ||
| /* | ||
| Copyright (C) 2021 Skandinaviska Enskilda Banken AB (publ) | ||
| 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 | ||
| <[email protected]>. 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. | ||
| */ | ||
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| /*! \file ql/pricingengines/asian/turnbullwakemanasianengine.hpp | ||
| \brief Turnbull Wakeman moment-matching Asian option Engine | ||
| \ingroup asianengines | ||
| */ | ||
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| #ifndef quantlib_turnbull_wakeman_asian_engine_hpp | ||
| #define quantlib_turnbull_wakeman_asian_engine_hpp | ||
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| #include <ql/instruments/asianoption.hpp> | ||
| #include <ql/processes/blackscholesprocess.hpp> | ||
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| namespace QuantLib { | ||
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| /*! Turnbull Wakeman two moment-matching Asian option Engine | ||
| Analytical pricing based on the two-moment Turnbull-Wakeman | ||
| approximation. | ||
| References: "Commodity Option Pricing", Iain Clark, Wiley, section 2.7.4. | ||
| "Option Pricing Formulas, Second Edition", E.G. Haug, 2006, pp. 192-202. | ||
| Some parts of the implementation were modeled after calculations from the | ||
| CommodityAveragePriceOptionAnalyticalEngine class in Open Source Risk Engine | ||
| (https://github.com/OpenSourceRisk/Engine). | ||
| \test | ||
| - the correctness of the returned value is tested by reproducing | ||
| results in literature with flat as well as upward and downward | ||
| sloping volatility term structures. | ||
| - the pricing of trades with guaranteed exercise/OTM is also tested. | ||
| */ | ||
| class TurnbullWakemanAsianEngine : public DiscreteAveragingAsianOption::engine { | ||
| public: | ||
| explicit TurnbullWakemanAsianEngine( | ||
| ext::shared_ptr<GeneralizedBlackScholesProcess> process) | ||
| : process_(process) { | ||
| registerWith(process_); | ||
| } | ||
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| void calculate() const; | ||
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| private: | ||
| ext::shared_ptr<GeneralizedBlackScholesProcess> process_; | ||
| }; | ||
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| } | ||
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| #endif |
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