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
|
/* -*- 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/math/functional.hpp>
#include <ql/instruments/payoffs.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/fdmblackscholesop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
namespace QuantLib {
FdmBlackScholesOp::FdmBlackScholesOp(
const boost::shared_ptr<FdmMesher>& mesher,
const boost::shared_ptr<GeneralizedBlackScholesProcess> & bsProcess,
Real strike,
bool localVol,
Real illegalLocalVolOverwrite,
Size direction)
: mesher_(mesher),
rTS_ (bsProcess->riskFreeRate().currentLink()),
qTS_ (bsProcess->dividendYield().currentLink()),
volTS_ (bsProcess->blackVolatility().currentLink()),
localVol_((localVol) ? bsProcess->localVolatility().currentLink()
: boost::shared_ptr<LocalVolTermStructure>()),
x_ ((localVol) ? Array(Exp(mesher->locations(direction))) : Array()),
dxMap_ (FirstDerivativeOp(direction, mesher)),
dxxMap_(SecondDerivativeOp(direction, mesher)),
mapT_ (direction, mesher),
strike_(strike),
illegalLocalVolOverwrite_(illegalLocalVolOverwrite),
direction_(direction) {
}
void FdmBlackScholesOp::setTime(Time t1, Time t2) {
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
if (localVol_) {
const boost::shared_ptr<FdmLinearOpLayout> layout=mesher_->layout();
const FdmLinearOpIterator endIter = layout->end();
Array v(layout->size());
for (FdmLinearOpIterator iter = layout->begin();
iter!=endIter; ++iter) {
const Size i = iter.index();
if (illegalLocalVolOverwrite_ < 0.0) {
v[i] = square<Real>()(
localVol_->localVol(0.5*(t1+t2), x_[i], true));
}
else {
try {
v[i] = square<Real>()(
localVol_->localVol(0.5*(t1+t2), x_[i], true));
} catch (Error&) {
v[i] = square<Real>()(illegalLocalVolOverwrite_);
}
}
}
mapT_.axpyb(r - q - 0.5*v, dxMap_,
dxxMap_.mult(0.5*v), Array(1, -r));
}
else {
const Real v
= volTS_->blackForwardVariance(t1, t2, strike_)/(t2-t1);
mapT_.axpyb(Array(1, r - q - 0.5*v), dxMap_,
dxxMap_.mult(0.5*Array(mesher_->layout()->size(), v)),
Array(1, -r));
}
}
Size FdmBlackScholesOp::size() const {
return mesher_->layout()->dim().size();
}
Disposable<Array> FdmBlackScholesOp::apply(const Array& u) const {
return mapT_.apply(u);
}
Disposable<Array> FdmBlackScholesOp::apply_direction(Size direction,
const Array& r) const {
if (direction == direction_)
return mapT_.apply(r);
else {
Array retVal(r.size(), 0.0);
return retVal;
}
}
Disposable<Array> FdmBlackScholesOp::apply_mixed(const Array& r) const {
Array retVal(r.size(), 0.0);
return retVal;
}
Disposable<Array> FdmBlackScholesOp::solve_splitting(Size direction,
const Array& r, Real dt) const {
if (direction == direction_)
return mapT_.solve_splitting(r, dt, 1.0);
else {
Array retVal(r);
return retVal;
}
}
Disposable<Array> FdmBlackScholesOp::preconditioner(const Array& r,
Real dt) const {
return solve_splitting(direction_, r, dt);
}
}
|
