| 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) 2018 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 analyticcevengine.hpp |
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| 21 | \brief Pricing engine for European vanilla options using a |
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| 22 | constant elasticity of variance (CEV) model |
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| 23 | */ |
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| 24 | |
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| 25 | #ifndef quantlib_analytic_cev_engine_hpp |
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| 26 | #define quantlib_analytic_cev_engine_hpp |
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| 27 | |
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| 28 | #include <ql/instruments/vanillaoption.hpp> |
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| 29 | #include <ql/termstructures/yieldtermstructure.hpp> |
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| 30 | |
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| 31 | namespace QuantLib { |
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| 32 | |
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| 33 | //! constant elasticity of variance process (absorbing boundary at f=0) |
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| 34 | /*! \f[ |
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| 35 | df_t = \alpha f_t^\beta \mathrm{d}W_t |
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| 36 | \f] |
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| 37 | */ |
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| 38 | |
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| 39 | /*! References: |
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| 40 | |
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| 41 | D.R. Brecher, A.E. Lindsay, Results on the CEV Process, Past and Present |
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| 42 | https://www.fincad.com/sites/default/files/wysiwyg/Resources-Wiki/cev-process-working-paper.pdf |
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| 43 | */ |
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| 44 | |
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| 45 | class CEVCalculator { |
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| 46 | public: |
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| 47 | CEVCalculator(Real f0, Real alpha, Real beta); |
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| 48 | |
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| 49 | Real value(Option::Type optionType, Real strike, Time t) const; |
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| 50 | |
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| 51 | Real f0() const { return f0_; } |
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| 52 | Real alpha() const { return alpha_; } |
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| 53 | Real beta() const { return beta_; } |
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| 54 | |
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| 55 | private: |
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| 56 | Real X(Real f) const; |
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| 57 | |
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| 58 | const Real f0_, alpha_, beta_, delta_, x0_; |
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| 59 | }; |
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| 60 | |
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| 61 | |
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| 62 | class AnalyticCEVEngine : public VanillaOption::engine { |
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| 63 | public: |
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| 64 | AnalyticCEVEngine(Real f0, Real alpha, Real beta, Handle<YieldTermStructure> discountCurve); |
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| 65 | |
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| 66 | void calculate() const override; |
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| 67 | |
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| 68 | private: |
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| 69 | const ext::shared_ptr<CEVCalculator> calculator_; |
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| 70 | const Handle<YieldTermStructure> discountCurve_; |
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| 71 | }; |
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| 72 | } |
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| 73 | |
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| 74 | #endif |
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| 75 | |
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