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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Giorgio Facchinetti
Copyright (C) 2010 Ferdinando Ametrano
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/indexes/iborindex.hpp>
#include <ql/instruments/makecapfloor.hpp>
#include <ql/math/solvers1d/brent.hpp>
#include <ql/pricingengines/capfloor/blackcapfloorengine.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/capfloor/capfloortermvolcurve.hpp>
#include <ql/termstructures/volatility/optionlet/optionletstripper1.hpp>
#include <ql/termstructures/volatility/optionlet/optionletstripper2.hpp>
#include <ql/termstructures/volatility/optionlet/spreadedoptionletvol.hpp>
#include <ql/termstructures/volatility/optionlet/strippedoptionletadapter.hpp>
#include <utility>
namespace QuantLib {
OptionletStripper2::OptionletStripper2(
const ext::shared_ptr<OptionletStripper1>& optionletStripper1,
const Handle<CapFloorTermVolCurve>& atmCapFloorTermVolCurve)
: OptionletStripper(optionletStripper1->termVolSurface(),
optionletStripper1->iborIndex(),
Handle<YieldTermStructure>(),
optionletStripper1->volatilityType(),
optionletStripper1->displacement(),
optionletStripper1->optionletFrequency()),
stripper1_(optionletStripper1), atmCapFloorTermVolCurve_(atmCapFloorTermVolCurve),
dc_(stripper1_->termVolSurface()->dayCounter()),
nOptionExpiries_(atmCapFloorTermVolCurve->optionTenors().size()),
atmCapFloorStrikes_(nOptionExpiries_), atmCapFloorPrices_(nOptionExpiries_),
spreadsVolImplied_(nOptionExpiries_), caps_(nOptionExpiries_) {
registerWith(stripper1_);
registerWith(atmCapFloorTermVolCurve_);
QL_REQUIRE(dc_ == atmCapFloorTermVolCurve->dayCounter(),
"different day counters provided");
}
void OptionletStripper2::performCalculations() const {
//// optionletStripper data
optionletDates_ = stripper1_->optionletFixingDates();
optionletPaymentDates_ = stripper1_->optionletPaymentDates();
optionletAccrualPeriods_ = stripper1_->optionletAccrualPeriods();
optionletTimes_ = stripper1_->optionletFixingTimes();
atmOptionletRate_ = stripper1_->atmOptionletRates();
for (Size i=0; i<optionletTimes_.size(); ++i) {
optionletStrikes_[i] = stripper1_->optionletStrikes(i);
optionletVolatilities_[i] = stripper1_->optionletVolatilities(i);
}
// atmCapFloorTermVolCurve data
const std::vector<Period>& optionExpiriesTenors =
atmCapFloorTermVolCurve_->optionTenors();
const std::vector<Time>& optionExpiriesTimes =
atmCapFloorTermVolCurve_->optionTimes();
for (Size j=0; j<nOptionExpiries_; ++j) {
Volatility atmOptionVol = atmCapFloorTermVolCurve_->volatility(
optionExpiriesTimes[j], 33.3333); // dummy strike
ext::shared_ptr<BlackCapFloorEngine> engine(new
BlackCapFloorEngine(iborIndex_->forwardingTermStructure(),
atmOptionVol, dc_));
caps_[j] = MakeCapFloor(CapFloor::Cap,
optionExpiriesTenors[j],
iborIndex_,
Null<Rate>(),
0*Days).withPricingEngine(engine);
atmCapFloorStrikes_[j] =
caps_[j]->atmRate(**iborIndex_->forwardingTermStructure());
atmCapFloorPrices_[j] = caps_[j]->NPV();
}
spreadsVolImplied_ = spreadsVolImplied();
StrippedOptionletAdapter adapter(stripper1_);
adapter.enableExtrapolation();
Volatility unadjustedVol, adjustedVol;
for (Size j=0; j<nOptionExpiries_; ++j) {
for (Size i=0; i<optionletVolatilities_.size(); ++i) {
if (i<=caps_[j]->floatingLeg().size()) {
unadjustedVol = adapter.volatility(optionletTimes_[i],
atmCapFloorStrikes_[j]);
adjustedVol = unadjustedVol + spreadsVolImplied_[j];
// insert adjusted volatility
auto previous =
std::lower_bound(optionletStrikes_[i].begin(),
optionletStrikes_[i].end(),
atmCapFloorStrikes_[j]);
Size insertIndex = previous - optionletStrikes_[i].begin();
optionletStrikes_[i].insert(
optionletStrikes_[i].begin() + insertIndex,
atmCapFloorStrikes_[j]);
optionletVolatilities_[i].insert(
optionletVolatilities_[i].begin() + insertIndex,
adjustedVol);
}
}
}
}
std::vector<Volatility> OptionletStripper2::spreadsVolImplied() const {
Brent solver;
std::vector<Volatility> result(nOptionExpiries_);
Volatility guess = 0.0001, minSpread = -0.1, maxSpread = 0.1;
for (Size j=0; j<nOptionExpiries_; ++j) {
ObjectiveFunction f(stripper1_, caps_[j], atmCapFloorPrices_[j]);
solver.setMaxEvaluations(maxEvaluations_);
Volatility root = solver.solve(f, accuracy_, guess,
minSpread, maxSpread);
result[j] = root;
}
return result;
}
std::vector<Volatility> OptionletStripper2::spreadsVol() const {
calculate();
return spreadsVolImplied_;
}
std::vector<Rate> OptionletStripper2::atmCapFloorStrikes() const{
calculate();
return atmCapFloorStrikes_;
}
std::vector<Real> OptionletStripper2::atmCapFloorPrices() const {
calculate();
return atmCapFloorPrices_;
}
//==========================================================================//
// OptionletStripper2::ObjectiveFunction //
//==========================================================================//
OptionletStripper2::ObjectiveFunction::ObjectiveFunction(
const ext::shared_ptr<OptionletStripper1>& optionletStripper1,
ext::shared_ptr<CapFloor> cap,
Real targetValue)
: cap_(std::move(cap)), targetValue_(targetValue) {
ext::shared_ptr<OptionletVolatilityStructure> adapter(new
StrippedOptionletAdapter(optionletStripper1));
adapter->enableExtrapolation();
// set an implausible value, so that calculation is forced
// at first operator()(Volatility x) call
spreadQuote_ = ext::make_shared<SimpleQuote>(-1.0);
ext::shared_ptr<OptionletVolatilityStructure> spreadedAdapter(new
SpreadedOptionletVolatility(Handle<OptionletVolatilityStructure>(
adapter), Handle<Quote>(spreadQuote_)));
ext::shared_ptr<BlackCapFloorEngine> engine(new
BlackCapFloorEngine(
optionletStripper1->iborIndex()->forwardingTermStructure(),
Handle<OptionletVolatilityStructure>(spreadedAdapter)));
cap_->setPricingEngine(engine);
}
Real OptionletStripper2::ObjectiveFunction::operator()(Volatility s) const
{
if (s!=spreadQuote_->value())
spreadQuote_->setValue(s);
return cap_->NPV()-targetValue_;
}
}
|
