| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2017 Klaus Spanderen |
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| 5 | |
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| 6 | This file is part of QuantLib, a free-software/open-source library |
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| 7 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 8 | |
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| 9 | QuantLib is free software: you can redistribute it and/or modify it |
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| 10 | under the terms of the QuantLib license. You should have received a |
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| 11 | copy of the license along with this program; if not, please email |
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| 12 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 13 | <http://quantlib.org/license.shtml>. |
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| 14 | |
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| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 17 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 18 | */ |
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| 19 | |
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| 20 | /*! \file coshestonengine.hpp |
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| 21 | \brief Heston engine based on Fourier-Cosine series expansions |
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| 22 | */ |
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| 23 | |
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| 24 | #ifndef quantlib_cos_heston_engine_hpp |
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| 25 | #define quantlib_cos_heston_engine_hpp |
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| 26 | |
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| 27 | #include <ql/models/equity/hestonmodel.hpp> |
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| 28 | #include <ql/instruments/vanillaoption.hpp> |
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| 29 | #include <ql/pricingengines/genericmodelengine.hpp> |
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| 30 | |
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| 31 | #include <complex> |
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| 32 | |
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| 33 | namespace QuantLib { |
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| 34 | |
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| 35 | //! COS-method Heston engine based on efficient Fourier series expansions |
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| 36 | |
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| 37 | /*! References: |
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| 38 | |
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| 39 | F. Fang, C.W. Oosterlee: A Novel Pricing Method for European Ooptions |
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| 40 | based on Fourier-Cosine Series Expansions, |
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| 41 | http://ta.twi.tudelft.nl/mf/users/oosterle/oosterlee/COS.pdf |
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| 42 | |
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| 43 | Fabien Le Floc'h: Fourier Integration and Stochastic Volatility |
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| 44 | Calibration, |
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| 45 | https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=2362968 |
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| 46 | |
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| 47 | \ingroup vanillaengines |
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| 48 | |
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| 49 | \test the correctness of the returned value is tested by |
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| 50 | reproducing results available in web/literature |
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| 51 | and comparison with Black pricing. |
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| 52 | */ |
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| 53 | class COSHestonEngine |
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| 54 | : public GenericModelEngine<HestonModel, |
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| 55 | VanillaOption::arguments, |
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| 56 | VanillaOption::results> { |
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| 57 | public: |
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| 58 | explicit COSHestonEngine(const ext::shared_ptr<HestonModel>& model, |
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| 59 | Real L = 16, Size N=200); |
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| 60 | |
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| 61 | void update() override; |
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| 62 | void calculate() const override; |
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| 63 | |
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| 64 | // normalized characteristic function |
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| 65 | std::complex<Real> chF(Real u, Real t) const; |
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| 66 | |
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| 67 | Real c1(Time t) const; |
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| 68 | Real c2(Time t) const; |
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| 69 | Real c3(Time t) const; |
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| 70 | Real c4(Time t) const; |
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| 71 | |
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| 72 | Real mu(Time t) const; |
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| 73 | Real var(Time t) const; |
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| 74 | Real skew(Time t) const; |
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| 75 | Real kurtosis(Time t) const; |
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| 76 | |
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| 77 | private: |
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| 78 | Real muT(Time t) const; |
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| 79 | |
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| 80 | const Real L_; |
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| 81 | const Size N_; |
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| 82 | Real kappa_, theta_, sigma_, rho_, v0_; |
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| 83 | }; |
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| 84 | } |
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| 85 | |
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| 86 | #endif |
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| 87 | |
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