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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Ferdinando Ametrano
Copyright (C) 2006 Marco Bianchetti
Copyright (C) 2006 Silvia Frasson
Copyright (C) 2006 Mario Pucci
Copyright (C) 2006 StatPro Italia srl
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/models/marketmodels/driftcomputation/lmmdriftcalculator.hpp>
#include <ql/models/marketmodels/curvestates/lmmcurvestate.hpp>
namespace QuantLib {
LMMDriftCalculator::LMMDriftCalculator(const Matrix& pseudo,
const std::vector<Spread>& displacements,
const std::vector<Time>& taus,
Size numeraire,
Size alive)
: numberOfRates_(taus.size()), numberOfFactors_(pseudo.columns()),
isFullFactor_(numberOfFactors_ == numberOfRates_), numeraire_(numeraire), alive_(alive),
displacements_(displacements), oneOverTaus_(taus.size()), pseudo_(pseudo),
tmp_(taus.size(), 0.0), e_(pseudo_.columns(), pseudo_.rows(), 0.0), downs_(taus.size()),
ups_(taus.size()) {
// Check requirements
QL_REQUIRE(numberOfRates_>0, "Dim out of range");
QL_REQUIRE(displacements.size() == numberOfRates_,
"Displacements out of range");
QL_REQUIRE(pseudo.rows()==numberOfRates_,
"pseudo.rows() not consistent with dim");
QL_REQUIRE(pseudo.columns()>0 && pseudo.columns()<=numberOfRates_,
"pseudo.rows() not consistent with pseudo.columns()");
QL_REQUIRE(alive<numberOfRates_, "Alive out of bounds");
QL_REQUIRE(numeraire_<=numberOfRates_, "Numeraire larger than dim");
QL_REQUIRE(numeraire_>=alive, "Numeraire smaller than alive");
// Precompute 1/taus
for (Size i=0; i<taus.size(); ++i)
oneOverTaus_[i] = 1.0/taus[i];
// Compute covariance matrix from pseudoroot
const Disposable<Matrix> pT = transpose(pseudo_);
C_ = pseudo_*pT;
// Compute lower and upper extrema for (non reduced) drift calculation
for (Size i=alive_; i<numberOfRates_; ++i) {
downs_[i] = std::min(i+1, numeraire_);
ups_[i] = std::max(i+1, numeraire_);
}
}
void LMMDriftCalculator::compute(const LMMCurveState& cs,
std::vector<Real>& drifts) const {
compute(cs.forwardRates(), drifts);
}
void LMMDriftCalculator::compute(const std::vector<Rate>& fwds,
std::vector<Real>& drifts) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(fwds.size()==numberOfRates_, "numberOfRates <> dim");
QL_REQUIRE(drifts.size()==numberOfRates_, "drifts.size() <> dim");
#endif
if (isFullFactor_)
computePlain(fwds, drifts);
else
computeReduced(fwds, drifts);
}
void LMMDriftCalculator::computePlain(const LMMCurveState& cs,
std::vector<Real>& drifts) const {
computePlain(cs.forwardRates(), drifts);
}
void LMMDriftCalculator::computePlain(const std::vector<Rate>& forwards,
std::vector<Real>& drifts) const {
// Compute drifts without factor reduction,
// using directly the covariance matrix.
// Precompute forwards factor
Size i;
for(i=alive_; i<numberOfRates_; ++i)
tmp_[i] = (forwards[i]+displacements_[i]) /
(oneOverTaus_[i]+forwards[i]);
// Compute drifts
for (i=alive_; i<numberOfRates_; ++i) {
drifts[i] = std::inner_product(tmp_.begin()+downs_[i],
tmp_.begin()+ups_[i],
C_.row_begin(i)+downs_[i], 0.0);
if (numeraire_>i+1)
drifts[i] = -drifts[i];
}
}
void LMMDriftCalculator::computeReduced(const LMMCurveState& cs,
std::vector<Real>& drifts) const {
computeReduced(cs.forwardRates(), drifts);
}
void LMMDriftCalculator::computeReduced(const std::vector<Rate>& forwards,
std::vector<Real>& drifts) const {
// Compute drifts with factor reduction,
// using the pseudo square root of the covariance matrix.
// Precompute forwards factor
for (Size i=alive_; i<numberOfRates_; ++i)
tmp_[i] = (forwards[i]+displacements_[i]) /
(oneOverTaus_[i]+forwards[i]);
// Enforce initialization
for (Size r=0; r<numberOfFactors_; ++r)
e_[r][std::max(0,static_cast<Integer>(numeraire_)-1)] = 0.0;
// Now compute drifts: take the numeraire P_N (numeraire_=N)
// as the reference point, divide the summation into 3 steps,
// et impera:
// 1st step: the drift corresponding to the numeraire P_N is zero.
// (if N=0 no drift is null, if N=numberOfRates_ the last drift is null).
if (numeraire_>0) drifts[numeraire_-1] = 0.0;
// 2nd step: then, move backward from N-2 (included) back to
// alive (included) (if N=0 jumps to 3rd step, if N=numberOfRates_ the
// e_[r][N-1] are correctly initialized):
for (Integer i=static_cast<Integer>(numeraire_)-2;
i>=static_cast<Integer>(alive_); --i) {
drifts[i] = 0.0;
for (Size r=0; r<numberOfFactors_; ++r) {
e_[r][i] = e_[r][i+1] + tmp_[i+1] * pseudo_[i+1][r];
drifts[i] -= e_[r][i]*pseudo_[i][r];
}
/*
Matrix::column_iterator p1 = e_.column_begin(i);
Matrix::column_iterator end = e_.column_end(i);
Matrix::const_column_iterator p2 = e_.column_begin(i+1);
Matrix::const_row_iterator q1 = pseudo_.row_begin(i);
Matrix::const_row_iterator q2 = pseudo_.row_begin(i+1);
Real x = tmp_[i+1];
while (p1 != end) {
*p1 = *p2 + x*(*q2);
drifts[i] -= *p1*(*q1);
++p1; ++p2; ++q1; ++q2;
}
*/
}
// 3rd step: now, move forward from N (included) up to n (excluded)
// (if N=0 this is the only relevant computation):
for (Size i=numeraire_; i<numberOfRates_; ++i) {
drifts[i] = 0.0;
for (Size r=0; r<numberOfFactors_; ++r) {
if (i==0)
e_[r][i] = tmp_[i] * pseudo_[i][r];
else
e_[r][i] = e_[r][i-1] + tmp_[i] * pseudo_[i][r];
drifts[i] += e_[r][i]*pseudo_[i][r];
}
}
}
}
|
