1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Andreas Gaida
Copyright (C) 2008, 2009 Ralph Schreyer
Copyright (C) 2008, 2009 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/processes/batesprocess.hpp>
#include <ql/pricingengines/vanilla/fdhestonvanillaengine.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/solvers/fdmhestonsolver.hpp>
#include <ql/methods/finitedifferences/meshers/fdmhestonvariancemesher.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmultistrikemesher.hpp>
namespace QuantLib {
FdHestonVanillaEngine::FdHestonVanillaEngine(
const boost::shared_ptr<HestonModel>& model,
Size tGrid, Size xGrid, Size vGrid, Size dampingSteps,
const FdmSchemeDesc& schemeDesc)
: GenericModelEngine<HestonModel,
DividendVanillaOption::arguments,
DividendVanillaOption::results>(model),
tGrid_(tGrid), xGrid_(xGrid),
vGrid_(vGrid), dampingSteps_(dampingSteps),
schemeDesc_(schemeDesc) {
}
FdmSolverDesc FdHestonVanillaEngine::getSolverDesc(Real) const {
// 1. Mesher
const boost::shared_ptr<HestonProcess> process = model_->process();
const Time maturity = process->time(arguments_.exercise->lastDate());
// 1.1 The variance mesher
const Size tGridMin = 5;
const boost::shared_ptr<FdmHestonVarianceMesher> varianceMesher(
new FdmHestonVarianceMesher(vGrid_, process,
maturity,std::max(tGridMin,tGrid_/50)));
// 1.2 The equity mesher
const boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
boost::shared_ptr<Fdm1dMesher> equityMesher;
if (strikes_.empty()) {
equityMesher = boost::shared_ptr<Fdm1dMesher>(
new FdmBlackScholesMesher(
xGrid_,
FdmBlackScholesMesher::processHelper(
process->s0(), process->dividendYield(),
process->riskFreeRate(), varianceMesher->volaEstimate()),
maturity, payoff->strike(),
Null<Real>(), Null<Real>(), 0.0001, 1.5,
std::pair<Real, Real>(payoff->strike(), 0.1)));
}
else {
QL_REQUIRE(arguments_.cashFlow.empty(),"multiple strikes engine "
"does not work with discrete dividends");
equityMesher = boost::shared_ptr<Fdm1dMesher>(
new FdmBlackScholesMultiStrikeMesher(
xGrid_,
FdmBlackScholesMesher::processHelper(
process->s0(), process->dividendYield(),
process->riskFreeRate(), varianceMesher->volaEstimate()),
maturity, strikes_, 0.0001, 1.5,
std::pair<Real, Real>(payoff->strike(), 0.075)));
}
const boost::shared_ptr<FdmMesher> mesher(
new FdmMesherComposite(equityMesher, varianceMesher));
// 2. Calculator
const boost::shared_ptr<FdmInnerValueCalculator> calculator(
new FdmLogInnerValue(arguments_.payoff, mesher, 0));
// 3. Step conditions
const boost::shared_ptr<FdmStepConditionComposite> conditions =
FdmStepConditionComposite::vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process->riskFreeRate()->referenceDate(),
process->riskFreeRate()->dayCounter());
// 4. Boundary conditions
const FdmBoundaryConditionSet boundaries;
// 5. Solver
FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
calculator, maturity,
tGrid_, dampingSteps_ };
return solverDesc;
}
void FdHestonVanillaEngine::calculate() const {
// cache lookup for precalculated results
for (Size i=0; i < cachedArgs2results_.size(); ++i) {
if ( cachedArgs2results_[i].first.exercise->type()
== arguments_.exercise->type()
&& cachedArgs2results_[i].first.exercise->dates()
== arguments_.exercise->dates()) {
boost::shared_ptr<PlainVanillaPayoff> p1 =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(
arguments_.payoff);
boost::shared_ptr<PlainVanillaPayoff> p2 =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(
cachedArgs2results_[i].first.payoff);
if (p1 && p1->strike() == p2->strike()
&& p1->optionType() == p2->optionType()) {
QL_REQUIRE(arguments_.cashFlow.empty(),
"multiple strikes engine does "
"not work with discrete dividends");
results_ = cachedArgs2results_[i].second;
return;
}
}
}
const boost::shared_ptr<HestonProcess> process = model_->process();
boost::shared_ptr<FdmHestonSolver> solver(new FdmHestonSolver(
Handle<HestonProcess>(process),
getSolverDesc(1.5), schemeDesc_));
const Real v0 = process->v0();
const Real spot = process->s0()->value();
results_.value = solver->valueAt(spot, v0);
results_.delta = solver->deltaAt(spot, v0);
results_.gamma = solver->gammaAt(spot, v0);
results_.theta = solver->thetaAt(spot, v0);
cachedArgs2results_.resize(strikes_.size());
const boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
for (Size i=0; i < strikes_.size(); ++i) {
cachedArgs2results_[i].first.exercise = arguments_.exercise;
cachedArgs2results_[i].first.payoff =
boost::shared_ptr<PlainVanillaPayoff>(
new PlainVanillaPayoff(payoff->optionType(), strikes_[i]));
const Real d = payoff->strike()/strikes_[i];
DividendVanillaOption::results&
results = cachedArgs2results_[i].second;
results.value = solver->valueAt(spot*d, v0)/d;
results.delta = solver->deltaAt(spot*d, v0);
results.gamma = solver->gammaAt(spot*d, v0)*d;
results.theta = solver->thetaAt(spot*d, v0)/d;
}
}
void FdHestonVanillaEngine::update() {
cachedArgs2results_.clear();
GenericModelEngine<HestonModel, DividendVanillaOption::arguments,
DividendVanillaOption::results>::update();
}
void FdHestonVanillaEngine::enableMultipleStrikesCaching(
const std::vector<Real>& strikes) {
strikes_ = strikes;
cachedArgs2results_.clear();
}
}
|
