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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 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
<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 fdmexpoujumpop.cpp
\brief Ornstein Uhlenbeck process plus jumps (Kluge Model)
*/
#include <ql/experimental/finitedifferences/fdmextendedornsteinuhlenbeckop.hpp>
#include <ql/experimental/finitedifferences/fdmextoujumpop.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
#include <ql/experimental/processes/extouwithjumpsprocess.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#if defined(QL_PATCH_MSVC)
#pragma warning(push)
#pragma warning(disable:4180)
#endif
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/operation.hpp>
#if defined(QL_PATCH_MSVC)
#pragma warning(pop)
#endif
namespace QuantLib {
FdmExtOUJumpOp::FdmExtOUJumpOp(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<ExtOUWithJumpsProcess>& process,
const ext::shared_ptr<YieldTermStructure>& rTS,
const FdmBoundaryConditionSet& bcSet,
Size integroIntegrationOrder)
: mesher_ (mesher),
process_(process),
rTS_ (rTS),
bcSet_ (bcSet),
gaussLaguerreIntegration_(integroIntegrationOrder),
x_ (mesher->locations(0)),
ouOp_ (new FdmExtendedOrnsteinUhlenbeckOp(
mesher,
process->getExtendedOrnsteinUhlenbeckProcess(), rTS, bcSet)),
dyMap_ (FirstDerivativeOp(1, mesher)
.mult(-process->beta()*mesher->locations(1)))
{
const Real eta = process_->eta();
const Real lambda = process_->jumpIntensity();
const Array yInt = gaussLaguerreIntegration_.x();
const Array weights= gaussLaguerreIntegration_.weights();
integroPart_ = SparseMatrix(mesher_->layout()->size(),
mesher_->layout()->size());
Array yLoc(mesher_->layout()->dim()[1]);
for (const auto& iter : *mesher_->layout()) {
yLoc[iter.coordinates()[1]] = mesher_->location(iter, 1);
}
for (const auto& iter : *mesher_->layout()) {
const Size diag = iter.index();
integroPart_(diag, diag) -= lambda;
const Real y = mesher_->location(iter, 1);
const Integer yIndex = iter.coordinates()[1];
for (Size i=0; i < yInt.size(); ++i) {
const Real weight = std::exp(-yInt[i])*weights[i];
const Real ys = y + yInt[i]/eta;
const Integer l = (ys > yLoc.back()) ? yLoc.size()-2
: std::upper_bound(yLoc.begin(),
yLoc.end()-1, ys) - yLoc.begin()-1;
const Real s = (ys-yLoc[l])/(yLoc[l+1]-yLoc[l]);
integroPart_(diag, mesher_->layout()->neighbourhood(iter, 1, l-yIndex))
+= weight*lambda*(1-s);
integroPart_(diag, mesher_->layout()->neighbourhood(iter, 1, l+1-yIndex))
+= weight*lambda*s;
}
}
}
Size FdmExtOUJumpOp::size() const {
return mesher_->layout()->dim().size();;
}
void FdmExtOUJumpOp::setTime(Time t1, Time t2) {
ouOp_->setTime(t1, t2);
}
Array FdmExtOUJumpOp::apply(const Array& r) const {
return ouOp_->apply(r) + dyMap_.apply(r) + integro(r);
}
Array FdmExtOUJumpOp::apply_mixed(const Array& r) const {
return integro(r);
}
Array FdmExtOUJumpOp::apply_direction(Size direction,
const Array& r) const {
if (direction == 0)
return ouOp_->apply_direction(direction, r);
else if (direction == 1)
return dyMap_.apply(r);
else {
return Array(r.size(), 0.0);
}
}
Array FdmExtOUJumpOp::solve_splitting(Size direction,
const Array& r, Real a) const {
if (direction == 0) {
return ouOp_->solve_splitting(direction, r, a);
}
else if (direction == 1) {
return dyMap_.solve_splitting(r, a, 1.0);
}
else {
return r;
}
}
Array FdmExtOUJumpOp::preconditioner(const Array& r, Real dt) const {
return ouOp_->solve_splitting(0, r, dt);
}
Array FdmExtOUJumpOp::integro(const Array& r) const {
return prod(integroPart_, r);
}
std::vector<SparseMatrix> FdmExtOUJumpOp::toMatrixDecomp() const {
QL_REQUIRE(bcSet_.empty(), "boundary conditions are not supported");
std::vector<SparseMatrix> retVal(1, ouOp_->toMatrixDecomp().front());
retVal.push_back(dyMap_.toMatrix());
retVal.push_back(integroPart_);
return retVal;
}
}
|
