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
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Allen Kuo
Copyright (C) 2010 Alessandro Roveda
Copyright (C) 2015 Andres Hernandez
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/math/bernsteinpolynomial.hpp>
#include <ql/termstructures/yield/nonlinearfittingmethods.hpp>
#include <utility>
namespace QuantLib {
ExponentialSplinesFitting::ExponentialSplinesFitting(
bool constrainAtZero,
const Array& weights,
const ext::shared_ptr<OptimizationMethod>& optimizationMethod,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
const Size numCoeffs,
const Real fixedKappa,
Constraint constraint)
: FittedBondDiscountCurve::FittingMethod(constrainAtZero, weights, optimizationMethod, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)),
numCoeffs_(numCoeffs), fixedKappa_(fixedKappa) {
QL_REQUIRE(ExponentialSplinesFitting::size() > 0, "At least 1 unconstrained coefficient required");
}
ExponentialSplinesFitting::ExponentialSplinesFitting(
bool constrainAtZero,
const Array& weights,
const Array& l2, const Real minCutoffTime, const Real maxCutoffTime,
const Size numCoeffs, const Real fixedKappa,
Constraint constraint)
: ExponentialSplinesFitting(constrainAtZero, weights, {}, l2,
minCutoffTime, maxCutoffTime,
numCoeffs, fixedKappa, std::move(constraint)) {}
ExponentialSplinesFitting::ExponentialSplinesFitting(
bool constrainAtZero,
const Size numCoeffs,
const Real fixedKappa,
const Array& weights,
Constraint constraint)
: ExponentialSplinesFitting(constrainAtZero, weights, {}, Array(),
0.0, QL_MAX_REAL,
numCoeffs, fixedKappa, std::move(constraint)) {}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod>
ExponentialSplinesFitting::clone() const {
return std::make_unique<ExponentialSplinesFitting>(*this);
}
Size ExponentialSplinesFitting::size() const {
Size N = constrainAtZero_ ? numCoeffs_ : numCoeffs_ + 1;
return (fixedKappa_ != Null<Real>()) ? N-1 : N; //One fewer optimization parameters if kappa is fixed
}
DiscountFactor ExponentialSplinesFitting::discountFunction(const Array& x,
Time t) const {
DiscountFactor d = 0.0;
Size N = size();
//Use the interal fixedKappa_ member if non-zero, otherwise take kappa from the passed x[] array
Real kappa = (fixedKappa_ != Null<Real>()) ? fixedKappa_: x[N-1];
Real coeff = 0;
if (!constrainAtZero_) {
for (Size i = 0; i < N - 1; ++i) {
d += x[i] * std::exp(-kappa * (i + 1) * t);
}
} else {
// notation:
// d(t) = coeff* exp(-kappa*1*t) + x[0]* exp(-kappa*2*t) +
// x[1]* exp(-kappa*3*t) + ..+ x[7]* exp(-kappa*9*t)
for (Size i = 0; i < N - 1; i++) {
d += x[i] * std::exp(-kappa * (i + 2) * t);
coeff += x[i];
}
coeff = 1.0 - coeff;
d += coeff * std::exp(-kappa * t);
}
return d;
}
NelsonSiegelFitting::NelsonSiegelFitting(
const Array& weights,
const ext::shared_ptr<OptimizationMethod>& optimizationMethod,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: FittedBondDiscountCurve::FittingMethod(true, weights, optimizationMethod, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)) {}
NelsonSiegelFitting::NelsonSiegelFitting(
const Array& weights,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: NelsonSiegelFitting(weights, {}, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)) {}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod>
NelsonSiegelFitting::clone() const {
return std::make_unique<NelsonSiegelFitting>(*this);
}
Size NelsonSiegelFitting::size() const {
return 4;
}
DiscountFactor NelsonSiegelFitting::discountFunction(const Array& x,
Time t) const {
Real kappa = x[size()-1];
Real zeroRate = x[0] + (x[1] + x[2])*
(1.0 - std::exp(-kappa*t))/
((kappa+QL_EPSILON)*(t+QL_EPSILON)) -
(x[2])*std::exp(-kappa*t);
DiscountFactor d = std::exp(-zeroRate * t) ;
return d;
}
SvenssonFitting::SvenssonFitting(const Array& weights,
const ext::shared_ptr<OptimizationMethod>& optimizationMethod,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: FittedBondDiscountCurve::FittingMethod(true, weights, optimizationMethod, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)) {}
SvenssonFitting::SvenssonFitting(const Array& weights,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: SvenssonFitting(weights, {}, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)) {}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod>
SvenssonFitting::clone() const {
return std::make_unique<SvenssonFitting>(*this);
}
Size SvenssonFitting::size() const {
return 6;
}
DiscountFactor SvenssonFitting::discountFunction(const Array& x,
Time t) const {
Real kappa = x[size()-2];
Real kappa_1 = x[size()-1];
Real zeroRate = x[0] + (x[1] + x[2])*
(1.0 - std::exp(-kappa*t))/
((kappa+QL_EPSILON)*(t+QL_EPSILON)) -
(x[2])*std::exp(-kappa*t) +
x[3]* (((1.0 - std::exp(-kappa_1*t))/((kappa_1+QL_EPSILON)*(t+QL_EPSILON)))- std::exp(-kappa_1*t));
DiscountFactor d = std::exp(-zeroRate * t) ;
return d;
}
CubicBSplinesFitting::CubicBSplinesFitting(
const std::vector<Time>& knots,
bool constrainAtZero,
const Array& weights,
const ext::shared_ptr<OptimizationMethod>& optimizationMethod,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: FittedBondDiscountCurve::FittingMethod(constrainAtZero, weights, optimizationMethod, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)),
splines_(3, knots.size() - 5, knots) {
QL_REQUIRE(knots.size() >= 8,
"At least 8 knots are required" );
Size basisFunctions = knots.size() - 4;
if (constrainAtZero) {
size_ = basisFunctions-1;
// Note: A small but nonzero N_th basis function at t=0 may
// lead to an ill conditioned problem
N_ = 1;
QL_REQUIRE(std::abs(splines_(N_, 0.0)) > QL_EPSILON,
"N_th cubic B-spline must be nonzero at t=0");
} else {
size_ = basisFunctions;
N_ = 0;
}
}
CubicBSplinesFitting::CubicBSplinesFitting(
const std::vector<Time>& knots,
bool constrainAtZero,
const Array& weights,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: CubicBSplinesFitting(knots, constrainAtZero, weights, {}, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)) {}
Real CubicBSplinesFitting::basisFunction(Integer i, Time t) const {
return splines_(i,t);
}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod>
CubicBSplinesFitting::clone() const {
return std::make_unique<CubicBSplinesFitting>(*this);
}
Size CubicBSplinesFitting::size() const {
return size_;
}
DiscountFactor CubicBSplinesFitting::discountFunction(const Array& x,
Time t) const {
DiscountFactor d = 0.0;
if (!constrainAtZero_) {
for (Size i=0; i<size_; ++i) {
d += x[i] * splines_(i,t);
}
} else {
const Real T = 0.0;
Real sum = 0.0;
for (Size i=0; i<size_; ++i) {
if (i < N_) {
d += x[i] * splines_(i,t);
sum += x[i] * splines_(i,T);
} else {
d += x[i] * splines_(i+1,t);
sum += x[i] * splines_(i+1,T);
}
}
Real coeff = 1.0 - sum;
coeff /= splines_(N_,T);
d += coeff * splines_(N_,t);
}
return d;
}
SimplePolynomialFitting::SimplePolynomialFitting(
Natural degree,
bool constrainAtZero,
const Array& weights,
const ext::shared_ptr<OptimizationMethod>& optimizationMethod,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: FittedBondDiscountCurve::FittingMethod(constrainAtZero, weights, optimizationMethod, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)),
size_(constrainAtZero ? degree : degree + 1) {}
SimplePolynomialFitting::SimplePolynomialFitting(
Natural degree,
bool constrainAtZero,
const Array& weights,
const Array& l2,
const Real minCutoffTime,
const Real maxCutoffTime,
Constraint constraint)
: SimplePolynomialFitting(degree, constrainAtZero, weights, {}, l2,
minCutoffTime, maxCutoffTime, std::move(constraint)) {}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod>
SimplePolynomialFitting::clone() const {
return std::make_unique<SimplePolynomialFitting>(*this);
}
Size SimplePolynomialFitting::size() const {
return size_;
}
DiscountFactor SimplePolynomialFitting::discountFunction(const Array& x,
Time t) const {
DiscountFactor d = 0.0;
if (!constrainAtZero_) {
for (Size i=0; i<size_; ++i)
d += x[i] * BernsteinPolynomial::get(i,i,t);
} else {
d = 1.0;
for (Size i=0; i<size_; ++i)
d += x[i] * BernsteinPolynomial::get(i+1,i+1,t);
}
return d;
}
SpreadFittingMethod::SpreadFittingMethod(const ext::shared_ptr<FittingMethod>& method,
Handle<YieldTermStructure> discountCurve,
const Real minCutoffTime,
const Real maxCutoffTime)
: FittedBondDiscountCurve::FittingMethod(
method != nullptr ? method->constrainAtZero() : true,
method != nullptr ? method->weights() : Array(),
method != nullptr ? method->optimizationMethod() : ext::shared_ptr<OptimizationMethod>(),
method != nullptr ? method->l2() : Array(),
minCutoffTime,
maxCutoffTime),
method_(method), discountingCurve_(std::move(discountCurve)) {
QL_REQUIRE(method, "Fitting method is empty");
QL_REQUIRE(!discountingCurve_.empty(), "Discounting curve cannot be empty");
}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod>
SpreadFittingMethod::clone() const {
return std::make_unique<SpreadFittingMethod>(*this);
}
Size SpreadFittingMethod::size() const {
return method_->size();
}
DiscountFactor SpreadFittingMethod::discountFunction(const Array& x, Time t) const{
return method_->discount(x, t)*discountingCurve_->discount(t, true)/rebase_;
}
void SpreadFittingMethod::init(){
//In case discount curve has a different reference date,
//discount to this curve's reference date
if (curve_->referenceDate() != discountingCurve_->referenceDate()){
rebase_ = discountingCurve_->discount(curve_->referenceDate());
}
else{
rebase_ = 1.0;
}
//Call regular init
FittedBondDiscountCurve::FittingMethod::init();
}
}
|
