1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2018 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 fdcevvanillaengine.hpp
21 \brief Finite-Differences pricing engine for the CEV model
22*/
23
24#include <ql/exercise.hpp>
25#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>
26#include <ql/methods/finitedifferences/meshers/fdmcev1dmesher.hpp>
27#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
28#include <ql/methods/finitedifferences/operators/fdmcevop.hpp>
29#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
30#include <ql/methods/finitedifferences/solvers/fdm1dimsolver.hpp>
31#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
32#include <ql/methods/finitedifferences/utilities/fdmdiscountdirichletboundary.hpp>
33#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
34#include <ql/methods/finitedifferences/utilities/fdmtimedepdirichletboundary.hpp>
35#include <ql/pricingengines/vanilla/analyticcevengine.hpp>
36#include <ql/pricingengines/vanilla/fdcevvanillaengine.hpp>
37#include <ql/termstructures/yieldtermstructure.hpp>
38#include <utility>
39
40namespace QuantLib {
41
42 namespace {
43 class PriceAtBoundary {
44 public:
45 PriceAtBoundary(Time maturityTime,
46 ext::shared_ptr<StrikedTypePayoff> payoff,
47 ext::shared_ptr<YieldTermStructure> rTS,
48 ext::shared_ptr<CEVCalculator> calculator)
49 : maturityTime_(maturityTime), payoff_(std::move(payoff)),
50 calculator_(std::move(calculator)), rTS_(std::move(rTS)) {}
51
52 Real operator()(Real t) const {
53 const Time time2Expiry = std::max(a: 1/365., b: maturityTime_ - t);
54 const DiscountFactor df =
55 rTS_->discount(t: maturityTime_) / rTS_->discount(t);
56
57 return df * calculator_->value(
58 optionType: payoff_->optionType(), strike: payoff_->strike(), t: time2Expiry);
59 }
60
61 private:
62 const Time maturityTime_;
63 const ext::shared_ptr<StrikedTypePayoff> payoff_;
64 const ext::shared_ptr<CEVCalculator> calculator_;
65 const ext::shared_ptr<YieldTermStructure> rTS_;
66 };
67 }
68
69 FdCEVVanillaEngine::FdCEVVanillaEngine(Real f0,
70 Real alpha,
71 Real beta,
72 Handle<YieldTermStructure> discountCurve,
73 Size tGrid,
74 Size xGrid,
75 Size dampingSteps,
76 Real scalingFactor,
77 Real eps,
78 const FdmSchemeDesc& schemeDesc)
79 : f0_(f0), alpha_(alpha), beta_(beta), discountCurve_(std::move(discountCurve)), tGrid_(tGrid),
80 xGrid_(xGrid), dampingSteps_(dampingSteps), scalingFactor_(scalingFactor), eps_(eps),
81 schemeDesc_(schemeDesc) {
82 registerWith(h: discountCurve_);
83 }
84
85 void FdCEVVanillaEngine::calculate() const {
86
87 // 1. Mesher
88 const ext::shared_ptr<StrikedTypePayoff> payoff =
89 ext::dynamic_pointer_cast<StrikedTypePayoff>(r: arguments_.payoff);
90 QL_REQUIRE(payoff, "non-striked payoff given");
91
92 const ext::shared_ptr<YieldTermStructure> rTS =
93 discountCurve_.currentLink();
94
95 const DayCounter dc = rTS->dayCounter();
96
97 const Date referenceDate = rTS->referenceDate();
98 const Date maturityDate = arguments_.exercise->lastDate();
99 const Time maturityTime = dc.yearFraction(d1: referenceDate, d2: maturityDate);
100
101 const ext::shared_ptr<Fdm1dMesher> cevMesher =
102 ext::make_shared<FdmCEV1dMesher>(
103 args: xGrid_,
104 args: f0_, args: alpha_, args: beta_,
105 args: maturityTime, args: eps_, args: scalingFactor_,
106 args: std::make_pair(x: payoff->strike(), y: 0.1));
107
108 const Real lowerBound = cevMesher->locations().front();
109 const Real upperBound = cevMesher->locations().back();
110
111 const ext::shared_ptr<FdmMesher> mesher =
112 ext::make_shared<FdmMesherComposite>(args: cevMesher);
113
114 // 2. Calculator
115 const ext::shared_ptr<FdmInnerValueCalculator> calculator =
116 ext::make_shared<FdmCellAveragingInnerValue>(args: payoff, args: mesher, args: 0);
117
118 // 3. Step conditions
119 const ext::shared_ptr<FdmStepConditionComposite> conditions =
120 FdmStepConditionComposite::vanillaComposite(
121 schedule: DividendSchedule(), exercise: arguments_.exercise,
122 mesher, calculator,
123 refDate: referenceDate, dayCounter: dc);
124
125 // 4. Boundary conditions
126 FdmBoundaryConditionSet boundaries;
127
128 const PriceAtBoundary upperBoundPrice(
129 maturityTime, payoff, rTS,
130 ext::make_shared<CEVCalculator>(args: upperBound, args: alpha_, args: beta_));
131
132 boundaries.push_back(x: ext::make_shared<FdmTimeDepDirichletBoundary>(
133 args: mesher, args: ext::function<Real (Real)>(upperBoundPrice),
134 args: 0, args: FdmTimeDepDirichletBoundary::Upper));
135
136 const Real delta = (1-2*beta_)/(1-beta_);
137 if (delta < 2.0) {
138 const Real terminalCashFlow = (*payoff)(lowerBound);
139
140 boundaries.push_back(
141 x: ext::make_shared<FdmDiscountDirichletBoundary>(
142 args: mesher, args: rTS, args: maturityTime, args: terminalCashFlow,
143 args: 0, args: FdmTimeDepDirichletBoundary::Lower));
144 }
145
146 // 5. Solver
147 const FdmSolverDesc solverDesc = {
148 .mesher: mesher, .bcSet: boundaries, .condition: conditions,
149 .calculator: calculator, .maturity: maturityTime, .timeSteps: tGrid_, .dampingSteps: dampingSteps_
150 };
151
152 const ext::shared_ptr<FdmLinearOpComposite> op =
153 ext::make_shared<FdmCEVOp>(
154 args: mesher, args: discountCurve_.currentLink(), args: f0_, args: alpha_, args: beta_, args: 0);
155
156 const ext::shared_ptr<Fdm1DimSolver> solver =
157 ext::make_shared<Fdm1DimSolver>(args: solverDesc, args: schemeDesc_, args: op);
158
159 results_.value = solver->interpolateAt(x: f0_);
160 results_.delta = solver->derivativeX(x: f0_);
161 results_.gamma = solver->derivativeXX(x: f0_);
162 results_.theta = solver->thetaAt(x: f0_);
163 }
164}
165

source code of quantlib/ql/pricingengines/vanilla/fdcevvanillaengine.cpp