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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2016 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 fdmornsteinuhlenbeckop.cpp
*/
#include <ql/math/functional.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/fdmornsteinuhlenbeckop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/processes/ornsteinuhlenbeckprocess.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
namespace QuantLib {
FdmOrnsteinUhlenbeckOp::FdmOrnsteinUhlenbeckOp(
const ext::shared_ptr<FdmMesher>& mesher,
ext::shared_ptr<OrnsteinUhlenbeckProcess> process,
ext::shared_ptr<YieldTermStructure> rTS,
Size direction)
: mesher_(mesher), process_(std::move(process)), rTS_(std::move(rTS)), direction_(direction),
m_(direction, mesher), mapX_(direction, mesher) {
Array drift(mesher_->layout()->size());
const Array x(mesher_->locations(direction));
for (const auto& iter : *mesher_->layout()) {
const Size i = iter.index();
drift[i] = process_->drift(0.0, x[i]);
}
m_.axpyb(drift, FirstDerivativeOp(direction, mesher),
SecondDerivativeOp(direction, mesher)
.mult(0.5*squared(process_->volatility())
*Array(mesher->layout()->size(), 1.0)), Array());
}
Size FdmOrnsteinUhlenbeckOp::size() const {
return mesher_->layout()->dim().size();;
}
void FdmOrnsteinUhlenbeckOp::setTime(Time t1, Time t2) {
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
mapX_.axpyb(Array(), m_, m_, Array(1, -r));
}
Array FdmOrnsteinUhlenbeckOp::apply(const Array& r) const {
return mapX_.apply(r);
}
Array FdmOrnsteinUhlenbeckOp::apply_mixed(const Array& r) const {
return Array(r.size(), 0.0);
}
Array FdmOrnsteinUhlenbeckOp::apply_direction(Size direction, const Array& r) const {
if (direction == direction_) {
return mapX_.apply(r);
}
else {
return Array(r.size(), 0.0);
}
}
Array FdmOrnsteinUhlenbeckOp::solve_splitting(Size direction, const Array& r, Real a) const {
if (direction == direction_) {
return mapX_.solve_splitting(r, a, 1.0);
}
else {
return r;
}
}
Array FdmOrnsteinUhlenbeckOp::preconditioner(const Array& r, Real dt) const {
return solve_splitting(direction_, r, dt);
}
std::vector<SparseMatrix> FdmOrnsteinUhlenbeckOp::toMatrixDecomp() const {
return std::vector<SparseMatrix>(1, mapX_.toMatrix());
}
}
|
