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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Mark Joshi
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.
*/
#include <ql/models/marketmodels/forwardforwardmappings.hpp>
#include <ql/models/marketmodels/curvestate.hpp>
#include <ql/models/marketmodels/curvestates/lmmcurvestate.hpp>
#include <vector>
namespace QuantLib {
Matrix ForwardForwardMappings::ForwardForwardJacobian(const CurveState& cs,
Size multiplier,
Size offset) {
Size n = cs.numberOfRates();
QL_REQUIRE(offset < multiplier, "offset must be less than period in"
" forward forward mappings");
Size k = (n-offset)/multiplier;
const std::vector<Time>& tau = cs.rateTaus();
Matrix jacobian = Matrix(k, n, 0.0);
Size m=offset;
for (Size l=0; l < k; ++l)
{
Real df = cs.discountRatio(m,m+multiplier);
Real bigTau = cs.rateTimes()[m+multiplier]
- cs.rateTimes()[m];
for (Size r=0; r < multiplier; ++r, ++m)
{
Real value = df * tau[m]*cs.discountRatio(m+1,m)-1;
value /= bigTau;
jacobian[l][m]=-value;
}
}
return jacobian;
}
Matrix ForwardForwardMappings::YMatrix(const CurveState& cs,
const std::vector<Spread>& shortDisplacements,
const std::vector<Spread>& longDisplacements,
Size multiplier,
Size offset) {
Size n = cs.numberOfRates();
QL_REQUIRE(offset < multiplier, "offset must be less than period in"
" forward forward mappings");
Size k = (n-offset)/multiplier;
QL_REQUIRE(shortDisplacements.size() == n , "shortDisplacements must be of size"
" equal to number of rates");
QL_REQUIRE(longDisplacements.size() == k , "longDisplacements must be of size"
" equal to (number of rates minus offset) divided by multiplier");
Matrix jacobian(ForwardForwardJacobian(cs,multiplier,offset));
for (Size i=0; i < k ; ++i)
{
Real tau = cs.rateTimes()[(i+1)*multiplier+offset]
- cs.rateTimes()[i*multiplier+offset];
Real longForward = (cs.discountRatio((i+1)*multiplier+offset,i*multiplier+offset)-1.0)
/tau;
Real longForwardDisplaced = longForward+ longDisplacements[i];
for (Size j=0; j < n; ++j)
{
Real shortForward = cs.forwardRate(j);
Real shortForwardDisplaced = shortForward+shortDisplacements[j];
jacobian[i][j] *= shortForwardDisplaced/longForwardDisplaced;
}
}
return jacobian;
}
LMMCurveState ForwardForwardMappings::RestrictCurveState(const CurveState& cs,
Size multiplier,
Size offset) {
Size n = cs.numberOfRates();
QL_REQUIRE(offset < multiplier, "offset must be less than period in"
" forward forward mappings");
Size k = (n-offset)/multiplier;
std::vector<Time> times(k+1);
std::vector<DiscountFactor> discRatios(k+1);
for (Size i=0; i < k+1; ++i)
{
times[i] = cs.rateTimes()[i*multiplier+offset];
discRatios[i] = cs.discountRatio(i*multiplier+offset,0);
}
LMMCurveState newState(times);
newState.setOnDiscountRatios(discRatios);
return newState;
}
}
|
