1 /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2 
3 /*
4  Copyright (C) 2014, 2015 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.cpp
21     \brief Analytic engine for arbitrary European payoffs under the Heston model
22 */
23 
24 #include <ql/math/integrals/gausslobattointegral.hpp>
25 #include <ql/methods/finitedifferences/utilities/hestonrndcalculator.hpp>
26 #include <ql/experimental/exoticoptions/analyticpdfhestonengine.hpp>
27 #include <ql/functional.hpp>
28 
29 namespace QuantLib {
30 
AnalyticPDFHestonEngine(const ext::shared_ptr<HestonModel> & model,Real integrationEps_,Size maxIntegrationIterations)31     AnalyticPDFHestonEngine::AnalyticPDFHestonEngine(
32         const ext::shared_ptr<HestonModel>& model,
33         Real integrationEps_,
34         Size maxIntegrationIterations)
35     : maxIntegrationIterations_(maxIntegrationIterations),
36       integrationEps_(integrationEps_),
37       model_(model) {  }
38 
calculate() const39     void AnalyticPDFHestonEngine::calculate() const {
40         using namespace ext::placeholders;
41 
42         // this is an European option pricer
43         QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
44                    "not an European option");
45 
46         const ext::shared_ptr<HestonProcess>& process = model_->process();
47 
48         const Time t = process->time(arguments_.exercise->lastDate());
49 
50         const Real xMax = 8.0 * std::sqrt(process->theta()*t
51             + (process->v0() - process->theta())
52                 *(1-std::exp(-process->kappa()*t))/process->kappa());
53 
54         const Real x0 = std::log(process->s0()->value());
55         const Real rD = process->riskFreeRate()->discount(t);
56         const Real qD = process->dividendYield()->discount(t);
57 
58         const Real drift = x0 + std::log(rD/qD);
59 
60         results_.value = GaussLobattoIntegral(
61             maxIntegrationIterations_, integrationEps_)(
62             ext::bind(&AnalyticPDFHestonEngine::weightedPayoff, this,_1, t),
63                          -xMax+drift, xMax+drift);
64     }
65 
Pv(Real x_t,Time t) const66     Real AnalyticPDFHestonEngine::Pv(Real x_t, Time t) const {
67         return HestonRNDCalculator(
68             model_->process(), integrationEps_, maxIntegrationIterations_)
69                 .pdf(x_t, t);
70     }
71 
cdf(Real s,Time t) const72     Real AnalyticPDFHestonEngine::cdf(Real s, Time t) const {
73         const Real x_t = std::log(s);
74         return HestonRNDCalculator(
75             model_->process(), integrationEps_, maxIntegrationIterations_)
76                 .cdf(x_t, t);
77     }
78 
weightedPayoff(Real x_t,Time t) const79     Real AnalyticPDFHestonEngine::weightedPayoff(Real x_t, Time t) const {
80         const DiscountFactor rD
81             = model_->process()->riskFreeRate()->discount(t);
82 
83         const Real s_t = std::exp(x_t);
84         const Real payoff = (*arguments_.payoff)(s_t);
85 
86         return (payoff != 0.0) ? payoff*Pv(x_t, t)*rD : 0.0;
87     }
88 }
89 
90