1 /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2 
3 /*
4  Copyright (C) 2014 Klaus Spanderen
5 
6  This file is part of QuantLib, a free-software/open-source library
7  for financial quantitative analysts and developers - http://quantlib.org/
8 
9  QuantLib is free software: you can redistribute it and/or modify it
10  under the terms of the QuantLib license.  You should have received a
11  copy of the license along with this program; if not, please email
12  <quantlib-dev@lists.sf.net>. The license is also available online at
13  <http://quantlib.org/license.shtml>.
14 
15  This program is distributed in the hope that it will be useful, but WITHOUT
16  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17  FOR A PARTICULAR PURPOSE.  See the license for more details.
18 */
19 
20 /*! \file analyticpdfhestonengine.hpp
21     \brief Analytic engine for arbitrary European payoffs under the Heston model
22 */
23 
24 #ifndef quantlib_analytic_pdf_heston_engine_hpp
25 #define quantlib_analytic_pdf_heston_engine_hpp
26 
27 #include <ql/instruments/vanillaoption.hpp>
28 #include <ql/models/equity/hestonmodel.hpp>
29 #include <ql/pricingengines/genericmodelengine.hpp>
30 
31 namespace QuantLib {
32 
33     //! Analytic engine for arbitrary European payoffs under the Heston model
34 
35     /*! References:
36 
37         The formulas are taken from A. Dragulescu, V. Yakovenko, 2002.
38         Probability distribution of returns in the Heston model
39         with stochastic volatility.
40         http://arxiv.org/pdf/cond-mat/0203046.pdf
41 
42         \test the correctness of the returned value is tested by
43               reproducing digital prices using call spreads and the
44               AnalyticHestonEngine.
45 
46     */
47     class AnalyticPDFHestonEngine
48        : public GenericModelEngine<HestonModel,
49                                    VanillaOption::arguments,
50                                    VanillaOption::results> {
51       public:
52         explicit AnalyticPDFHestonEngine(const ext::shared_ptr<HestonModel>& model,
53                                          Real gaussLobattoEps = 1e-6,
54                                          Size gaussLobattoIntegrationOrder = 10000UL);
55         void calculate() const;
56 
57 
58         // probability in x_t = ln(s_t)
59         Real Pv(Real x_t, Time t) const;
60 
61         // cumulative distribution function Pr(x < X)
62         Real cdf(Real X, Time t) const;
63 
64       private:
65         Real weightedPayoff(Real x_t, Time t) const;
66 
67         const Size maxIntegrationIterations_;
68         const Real integrationEps_;
69 
70         const ext::shared_ptr<HestonModel> model_;
71     };
72 }
73 
74 
75 #endif
76