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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 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
<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/experimental/volatility/sabrvolsurface.hpp>
#include <ql/termstructures/volatility/smilesection.hpp>
#include <ql/math/interpolations/sabrinterpolation.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/quotes/simplequote.hpp>
namespace QuantLib {
SabrVolSurface::SabrVolSurface(
const boost::shared_ptr<InterestRateIndex>& index,
const Handle<BlackAtmVolCurve>& atmCurve,
const std::vector<Period>& optionTenors,
const std::vector<Spread>& atmRateSpreads,
const std::vector<std::vector<Handle<Quote> > >& volSpreads)
: InterestRateVolSurface(index),
atmCurve_(atmCurve),
optionTenors_(optionTenors),
optionTimes_(optionTenors.size()),
optionDates_(optionTenors.size()),
atmRateSpreads_(atmRateSpreads),
volSpreads_(volSpreads) {
checkInputs();
// Creation of reference smile sections
// Hard coded
isAlphaFixed_ = false;
isBetaFixed_ = false;
isNuFixed_ = false;
isRhoFixed_ = false;
vegaWeighted_ = true;
sabrGuesses_.resize(optionTenors_.size());
for (Size i=0; i<optionTenors_.size(); ++i) {
optionDates_[i] = optionDateFromTenor(optionTenors_[i]);
optionTimes_[i] = timeFromReference(optionDates_[i]);
// Hard coded
sabrGuesses_[i][0] = 0.025; // alpha
sabrGuesses_[i][1] = 0.5; // beta
sabrGuesses_[i][2] = 0.3; // rho
sabrGuesses_[i][3] = 0.0; // nu
}
registerWithMarketData();
}
boost::array<Real, 4> SabrVolSurface::sabrGuesses(const Date& d) const {
// the guesses for sabr parameters are assumed to be piecewise constant
if (d<=optionDates_[0]) return sabrGuesses_[0];
Size i=0;
while( d<optionDates_[i] && i<optionDates_.size()-1)
++i;
return sabrGuesses_[i];
}
void SabrVolSurface::updateSabrGuesses(const Date& d, boost::array<Real, 4> newGuesses) const {
Size i=0;
while( d<=optionDates_[i] && i<optionDates_.size())
++i;
sabrGuesses_[i][0] = newGuesses[0];
sabrGuesses_[i][1] = newGuesses[1];
sabrGuesses_[i][2] = newGuesses[2];
sabrGuesses_[i][3] = newGuesses[3];
}
std::vector<Volatility> SabrVolSurface::volatilitySpreads(const Date& d) const {
Size nOptionsTimes = optionTimes_.size();
Size nAtmRateSpreads = atmRateSpreads_.size();
std::vector<Volatility> interpolatedVols(nAtmRateSpreads);
std::vector<Volatility> vols(nOptionsTimes); // the volspread at a given strike
for (Size i=0; i<nAtmRateSpreads; ++i) {
for (Size j=0; j<nOptionsTimes; ++j) {
vols[j] = (**volSpreads_[j][i]).value();
}
LinearInterpolation interpolator(optionTimes_.begin(), optionTimes_.end(),
vols.begin());
interpolatedVols[i] = interpolator(timeFromReference(d),true);
}
return interpolatedVols;
}
void SabrVolSurface::update() {
TermStructure::update();
for (Size i=0; i<optionTenors_.size(); ++i) {
optionDates_[i] = optionDateFromTenor(optionTenors_[i]);
optionTimes_[i] = timeFromReference(optionDates_[i]);
}
notifyObservers();
}
boost::shared_ptr<SmileSection>
SabrVolSurface::smileSectionImpl(Time t) const {
BigInteger n = BigInteger(t*365.0);
Date d = referenceDate()+n*Days;
// interpolating on ref smile sections
std::vector<Volatility> volSpreads = volatilitySpreads(d);
// calculate sabr fit
boost::array<Real, 4> sabrParameters1 = sabrGuesses(d);
boost::shared_ptr<SabrInterpolatedSmileSection> tmp(new
SabrInterpolatedSmileSection(d,
index_->fixing(d,true), atmRateSpreads_, true,
atmCurve_->atmVol(d), volSpreads,
sabrParameters1[0], sabrParameters1[1],
sabrParameters1[2], sabrParameters1[3],
isAlphaFixed_, isBetaFixed_,
isNuFixed_, isRhoFixed_,
vegaWeighted_/*,
const boost::shared_ptr<EndCriteria>& endCriteria,
const boost::shared_ptr<OptimizationMethod>& method,
const DayCounter& dc*/));
// update guess
return tmp;
}
void SabrVolSurface::registerWithMarketData() {
for (Size i=0; i<optionTenors_.size(); ++i) {
for (Size j=0; j<atmRateSpreads_.size(); ++j) {
registerWith(volSpreads_[i][j]);
}
}
}
void SabrVolSurface::checkInputs() const {
Size nStrikes = atmRateSpreads_.size();
QL_REQUIRE(nStrikes>1, "too few strikes (" << nStrikes << ")");
for (Size i=1; i<nStrikes; ++i)
QL_REQUIRE(atmRateSpreads_[i-1]<atmRateSpreads_[i],
"non increasing strike spreads: " <<
io::ordinal(i) << " is " << atmRateSpreads_[i-1] << ", " <<
io::ordinal(i+1) << " is " << atmRateSpreads_[i]);
for (Size i=0; i<volSpreads_.size(); i++)
QL_REQUIRE(atmRateSpreads_.size()==volSpreads_[i].size(),
"mismatch between number of strikes (" << atmRateSpreads_.size() <<
") and number of columns (" << volSpreads_[i].size() <<
") in the " << io::ordinal(i+1) << " row");
}
void SabrVolSurface::accept(AcyclicVisitor& v) {
Visitor<SabrVolSurface>* v1 =
dynamic_cast<Visitor<SabrVolSurface>*>(&v);
if (v1 != 0)
v1->visit(*this);
else
InterestRateVolSurface::accept(v);
}
}
|
