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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 Klaus Spanderen
Copyright (C) 2014 Ralph Schreyer
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
<https://www.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.
*/
/*! \file fdsimpleextoustorageengine.cpp
\brief Finite Differences extended OU engine for simple storage options
*/
#include <ql/experimental/finitedifferences/fdmexpextouinnervaluecalculator.hpp>
#include <ql/experimental/finitedifferences/fdmsimple2dextousolver.hpp>
#include <ql/experimental/finitedifferences/fdsimpleextoustorageengine.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
#include <ql/math/comparison.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmsimpleprocess1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/predefined1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsolverdesc.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsimplestoragecondition.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/pricingengines/vanilla/fdsimplebsswingengine.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
namespace QuantLib {
namespace {
class FdmStorageValue : public FdmInnerValueCalculator {
public:
explicit FdmStorageValue(ext::shared_ptr<FdmMesher> mesher)
: mesher_(std::move(mesher)) {}
Real innerValue(const FdmLinearOpIterator& iter, Time) override {
const Real s = std::exp(mesher_->location(iter, 0));
const Real v = mesher_->location(iter, 1);
return s*v;
}
Real avgInnerValue(const FdmLinearOpIterator& iter, Time t) override {
return innerValue(iter, t);
}
private:
const ext::shared_ptr<FdmMesher> mesher_;
};
class LessButNotCloseEnough {
public:
bool operator()(Real a, Real b) const {
return !(close_enough(a, b, 100) || b < a);
}
};
}
FdSimpleExtOUStorageEngine::FdSimpleExtOUStorageEngine(
ext::shared_ptr<ExtendedOrnsteinUhlenbeckProcess> process,
ext::shared_ptr<YieldTermStructure> rTS,
Size tGrid,
Size xGrid,
Size yGrid,
ext::shared_ptr<Shape> shape,
const FdmSchemeDesc& schemeDesc)
: process_(std::move(process)), rTS_(std::move(rTS)), tGrid_(tGrid), xGrid_(xGrid),
yGrid_(yGrid), shape_(std::move(shape)), schemeDesc_(schemeDesc) {}
void FdSimpleExtOUStorageEngine::calculate() const {
// 1. Exercise
QL_REQUIRE(arguments_.exercise->type() == Exercise::Bermudan,
"Bermudan exercise supported only");
// 2. Mesher
const Time maturity
= rTS_->dayCounter().yearFraction(rTS_->referenceDate(),
arguments_.exercise->lastDate());
const ext::shared_ptr<Fdm1dMesher> xMesher(
new FdmSimpleProcess1dMesher(xGrid_, process_, maturity));
ext::shared_ptr<Fdm1dMesher> storageMesher;
if(yGrid_ == Null<Size>()){
//elevator mesher
std::vector<Real> storageValues(1, arguments_.capacity);
storageValues.reserve(
Size(arguments_.capacity/arguments_.changeRate)+1);
for (Real level=0; level <= arguments_.capacity;
level+=arguments_.changeRate) {
storageValues.push_back(level);
storageValues.push_back(arguments_.capacity - level);
}
const std::set<Real, LessButNotCloseEnough> orderedValues(
storageValues.begin(), storageValues.end());
storageValues.assign(orderedValues.begin(), orderedValues.end());
storageMesher = ext::shared_ptr<Fdm1dMesher>(
new Predefined1dMesher(storageValues));
}
else {
// uniform mesher
storageMesher = ext::shared_ptr<Fdm1dMesher>(
new Uniform1dMesher(0, arguments_.capacity, yGrid_));
}
const ext::shared_ptr<FdmMesher> mesher (
new FdmMesherComposite(xMesher, storageMesher));
// 3. Calculator
ext::shared_ptr<FdmInnerValueCalculator> storageCalculator(
new FdmStorageValue(mesher));
// 4. Step conditions
std::list<ext::shared_ptr<StepCondition<Array> > > stepConditions;
std::list<std::vector<Time> > stoppingTimes;
// 4.1 Bermudan step conditions
std::vector<Time> exerciseTimes;
for (auto i : arguments_.exercise->dates()) {
const Time t = rTS_->dayCounter().yearFraction(rTS_->referenceDate(), i);
QL_REQUIRE(t >= 0, "exercise dates must not contain past date");
exerciseTimes.push_back(t);
}
stoppingTimes.push_back(exerciseTimes);
ext::shared_ptr<Payoff> payoff(
new PlainVanillaPayoff(Option::Call, 0.0));
ext::shared_ptr<FdmInnerValueCalculator> underlyingCalculator(
new FdmExpExtOUInnerValueCalculator(payoff, mesher, shape_));
stepConditions.push_back(ext::shared_ptr<StepCondition<Array> >(
new FdmSimpleStorageCondition(exerciseTimes,
mesher, underlyingCalculator,
arguments_.changeRate)));
ext::shared_ptr<FdmStepConditionComposite> conditions(
new FdmStepConditionComposite(stoppingTimes, stepConditions));
// 5. Boundary conditions
const FdmBoundaryConditionSet boundaries;
// 6. Solver
FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
storageCalculator, maturity, tGrid_, 0 };
ext::shared_ptr<FdmSimple2dExtOUSolver> solver(
new FdmSimple2dExtOUSolver(
Handle<ExtendedOrnsteinUhlenbeckProcess>(process_),
rTS_, solverDesc, schemeDesc_));
const Real x = process_->x0();
const Real y = arguments_.load;
results_.value = solver->valueAt(x, y);
}
}
|
