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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2020, 2025 Marcin Rybacki
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 ultimateforwardtermstructure.hpp
\brief Ultimate Forward Rate term structure
*/
#ifndef quantlib_ultimate_forward_term_structure_hpp
#define quantlib_ultimate_forward_term_structure_hpp
#include <ql/math/rounding.hpp>
#include <ql/optional.hpp>
#include <ql/quote.hpp>
#include <ql/termstructures/yield/zeroyieldstructure.hpp>
#include <utility>
namespace QuantLib {
//! Ultimate forward term structure
/*! Dutch regulatory term structure for pension funds with a
parametrized extrapolation mechanism designed for
discounting long dated liabilities.
Relevant documentation can be found on the Dutch Central
Bank website:
FTK term structure documentation (Financieel toetsingskader):
https://www.dnb.nl/media/4lmprzrk/vaststelling_methode_rentetermijnstructuur_ftk.pdf
UFR 2013-2019 term structure documentation:
https://www.dnb.nl/media/0vmbxaf4/methodologie-dnb.pdf
UFR 2023 term structure documentation (p.46):
https://www.tweedekamer.nl/downloads/document?id=2022D50944
Optionally, computed zero rates may be rounded.
The specified number of decimal places will affect the rate
in decimal format; for example, rounding a rate of 1.5555%
to 5 decimal places results in 0.015555 becoming 0.01556, or 1.556%.
This term structure will remain linked to the original
structure, i.e., any changes in the latter will be
reflected in this structure as well.
\ingroup yieldtermstructures
\test
- the correctness of the returned zero rates is tested by
checking them against reference values obtained
from the official source.
- extrapolated forward is validated.
- rates on the cut-off point are checked against those
implied by the base curve.
- inspectors are tested against the base curve.
- incorrect input for cut-off point should raise an exception.
- observability against changes in the underlying term
structure and the additional components is checked.
- rounding of output rate with predefined compounding.
*/
class UltimateForwardTermStructure : public ZeroYieldStructure {
public:
UltimateForwardTermStructure(Handle<YieldTermStructure>,
Handle<Quote> lastLiquidForwardRate,
Handle<Quote> ultimateForwardRate,
const Period& firstSmoothingPoint,
Real alpha,
const ext::optional<Integer>& roundingDigits = ext::nullopt,
Compounding compounding = Compounded,
Frequency frequency = Annual);
//! \name YieldTermStructure interface
//@{
DayCounter dayCounter() const override;
Calendar calendar() const override;
Natural settlementDays() const override;
const Date& referenceDate() const override;
Date maxDate() const override;
//@}
//! \name Observer interface
//@{
void update() override;
//@}
protected:
//! returns the UFR extended zero yield rate
Rate zeroYieldImpl(Time) const override;
//@}
private:
//! applies rounding on zero rate with required compounding
Rate applyRounding(Rate r, Time t) const;
//@}
Handle<YieldTermStructure> originalCurve_;
Handle<Quote> llfr_;
Handle<Quote> ufr_;
Period fsp_;
Real alpha_;
ext::optional<Integer> roundingDigits_;
Compounding compounding_;
Frequency frequency_;
};
// inline definitions
inline UltimateForwardTermStructure::UltimateForwardTermStructure(
Handle<YieldTermStructure> h,
Handle<Quote> lastLiquidForwardRate,
Handle<Quote> ultimateForwardRate,
const Period& firstSmoothingPoint,
Real alpha,
const ext::optional<Integer>& roundingDigits,
Compounding compounding,
Frequency frequency)
: originalCurve_(std::move(h)), llfr_(std::move(lastLiquidForwardRate)),
ufr_(std::move(ultimateForwardRate)), fsp_(firstSmoothingPoint), alpha_(alpha),
roundingDigits_(roundingDigits), compounding_(compounding), frequency_(frequency) {
QL_REQUIRE(fsp_.length() > 0,
"first smoothing point must be a period with positive length");
if (!originalCurve_.empty())
enableExtrapolation(originalCurve_->allowsExtrapolation());
registerWith(originalCurve_);
registerWith(llfr_);
registerWith(ufr_);
}
inline DayCounter UltimateForwardTermStructure::dayCounter() const {
return originalCurve_->dayCounter();
}
inline Calendar UltimateForwardTermStructure::calendar() const {
return originalCurve_->calendar();
}
inline Natural UltimateForwardTermStructure::settlementDays() const {
return originalCurve_->settlementDays();
}
inline const Date& UltimateForwardTermStructure::referenceDate() const {
return originalCurve_->referenceDate();
}
inline Date UltimateForwardTermStructure::maxDate() const { return Date::maxDate(); }
inline void UltimateForwardTermStructure::update() {
if (!originalCurve_.empty()) {
YieldTermStructure::update();
enableExtrapolation(originalCurve_->allowsExtrapolation());
} else {
/* The implementation inherited from YieldTermStructure
asks for our reference date, which we don't have since
the original curve is still not set. Therefore, we skip
over that and just call the base-class behavior. */
// NOLINTNEXTLINE(bugprone-parent-virtual-call)
TermStructure::update();
}
}
inline Rate UltimateForwardTermStructure::applyRounding(Rate r, Time t) const {
if (!roundingDigits_.has_value()) {
return r;
}
// Input rate is continuously compounded by definition.
// Hence, in case this is also the selected compounding method for rounding,
// it is not required to calculate equivalent rates, and rounding
// may be applied directly.
Rate equivalentRate = compounding_ == Continuous ?
r :
InterestRate(r, dayCounter(), Continuous, NoFrequency)
.equivalentRate(compounding_, frequency_, t);
Rate rounded = ClosestRounding(*roundingDigits_)(equivalentRate);
return compounding_ == Continuous ?
rounded :
InterestRate(rounded, dayCounter(), compounding_, frequency_)
.equivalentRate(Continuous, NoFrequency, t);
}
inline Rate UltimateForwardTermStructure::zeroYieldImpl(Time t) const {
Time cutOffTime = originalCurve_->timeFromReference(referenceDate() + fsp_);
Time deltaT = t - cutOffTime;
/* If time to maturity (T) exceeds the cut-off point (T_c),
i.e. the first smoothing point, the forward rate f is
extrapolated as follows:
f(t,T_c,T) = UFR(t) + (LLFR(t) - UFR(t)) * B(T-T_c),
where:
UFR(t) - Ultimate Forward Rate quote,
LLFR(t) - Last Liquid Forward Rate quote,
B(t-T_c) = [1 - exp(-a * (T-T_c))] / [a * (T-T_c)],
with a being the growth factor (alpha). */
if (deltaT > 0.0) {
InterestRate baseRate = originalCurve_->zeroRate(cutOffTime, Continuous, NoFrequency);
Real beta = (1.0 - std::exp(-alpha_ * deltaT)) / (alpha_ * deltaT);
Rate extrapolatedForward = ufr_->value() + (llfr_->value() - ufr_->value()) * beta;
return applyRounding((cutOffTime * baseRate + deltaT * extrapolatedForward) / t, t);
}
return applyRounding(originalCurve_->zeroRate(t, Continuous, NoFrequency), t);
}
}
#endif
|
