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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2013 Peter Caspers
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/models/smilesectionutils.hpp>
#include <ql/math/comparison.hpp>
namespace QuantLib {
SmileSectionUtils::SmileSectionUtils(const SmileSection §ion,
const std::vector<Real> &moneynessGrid,
const Real atm,
const bool deleteArbitragePoints) {
if (moneynessGrid.size() != 0) {
QL_REQUIRE(
moneynessGrid[0] >= 0.0,
"moneyness grid should only contain non negative values ("
<< moneynessGrid[0] << ")");
for (Size i = 0; i < moneynessGrid.size() - 1; i++) {
QL_REQUIRE(moneynessGrid[i] < moneynessGrid[i + 1],
"moneyness grid should contain strictly increasing "
"values ("
<< moneynessGrid[i] << ","
<< moneynessGrid[i + 1] << " at indices " << i
<< ", " << i + 1 << ")");
}
}
if (atm == Null<Real>()) {
f_ = section.atmLevel();
QL_REQUIRE(f_ != Null<Real>(),
"atm level must be provided by source section or given "
"in the constructor");
} else {
f_ = atm;
}
std::vector<Real> tmp;
static const Real defaultMoney[] = { 0.0, 0.01, 0.05, 0.10, 0.25, 0.40,
0.50, 0.60, 0.70, 0.80, 0.90, 1.0,
1.25, 1.5, 1.75, 2.0, 5.0, 7.5,
10.0, 15.0, 20.0 };
if (moneynessGrid.size() == 0)
tmp = std::vector<Real>(defaultMoney, defaultMoney + 21);
else
tmp = std::vector<Real>(moneynessGrid);
if (tmp[0] > QL_EPSILON) {
m_.push_back(0.0);
k_.push_back(0.0);
}
bool minStrikeAdded = false, maxStrikeAdded = false;
for (Size i = 0; i < tmp.size(); i++) {
Real k = tmp[i] * f_;
if (tmp[i] <= QL_EPSILON ||
(k >= section.minStrike() && k <= section.maxStrike())) {
if (!minStrikeAdded || !close(k, section.minStrike())) {
m_.push_back(tmp[i]);
k_.push_back(k);
}
if (close(k, section.maxStrike()))
maxStrikeAdded = true;
} else { // if the section provides a limited strike range
// we put the respective endpoint in our grid
// in order to not loose too much information
if (k < section.minStrike() && !minStrikeAdded) {
m_.push_back(section.minStrike() / f_);
k_.push_back(section.minStrike());
minStrikeAdded = true;
}
if (k > section.maxStrike() && !maxStrikeAdded) {
m_.push_back(section.maxStrike() / f_);
k_.push_back(section.maxStrike());
maxStrikeAdded = true;
}
}
}
c_.push_back(f_);
for (Size i = 1; i < k_.size(); i++) {
c_.push_back(section.optionPrice(k_[i], Option::Call, 1.0));
}
Size centralIndex =
std::upper_bound(m_.begin(), m_.end(), 1.0 - QL_EPSILON) -
m_.begin();
QL_REQUIRE(centralIndex < k_.size() - 1 && centralIndex > 1,
"Atm point in moneyness grid ("
<< centralIndex << ") too close to boundary.");
leftIndex_ = centralIndex;
rightIndex_ = centralIndex;
bool done = false;
while (!done) {
bool isAf = true;
done = true;
while (isAf && rightIndex_ < k_.size() - 1) {
rightIndex_++;
isAf = af(leftIndex_, rightIndex_, rightIndex_) &&
af(leftIndex_, rightIndex_ - 1, rightIndex_);
}
if (!isAf)
rightIndex_--;
isAf = true;
while (isAf && leftIndex_ > 1) {
leftIndex_--;
isAf = af(leftIndex_, leftIndex_, rightIndex_) &&
af(leftIndex_, leftIndex_ + 1, rightIndex_);
}
if (!isAf)
leftIndex_++;
if (rightIndex_ < leftIndex_)
rightIndex_ = leftIndex_;
if (deleteArbitragePoints && leftIndex_ > 1) {
m_.erase(m_.begin() + leftIndex_ - 1);
k_.erase(k_.begin() + leftIndex_ - 1);
c_.erase(c_.begin() + leftIndex_ - 1);
leftIndex_--;
rightIndex_--;
done = false;
}
if (deleteArbitragePoints && rightIndex_ < k_.size() - 1) {
m_.erase(m_.begin() + rightIndex_ + 1);
k_.erase(k_.begin() + rightIndex_ + 1);
c_.erase(c_.begin() + rightIndex_ + 1);
rightIndex_--;
done = false;
}
}
QL_REQUIRE(rightIndex_ > leftIndex_,
"arbitrage free region must at least contain two "
"points (only index is "
<< leftIndex_ << ")");
}
const std::pair<Real, Real> SmileSectionUtils::arbitragefreeRegion() const {
return std::pair<Real, Real>(k_[leftIndex_], k_[rightIndex_]);
}
const std::pair<Size, Size>
SmileSectionUtils::arbitragefreeIndices() const {
return std::pair<Size, Size>(leftIndex_, rightIndex_);
}
bool SmileSectionUtils::af(const Size i0, const Size i,
const Size i1) const {
if (i == 0)
return true;
Size im = i - 1 >= i0 ? i - 1 : 0;
Real q1 = (c_[i] - c_[im]) / (k_[i] - k_[im]);
if (q1 < -1.0 || q1 > 0.0)
return false;
if (i >= i1)
return true;
Real q2 = (c_[i + 1] - c_[i]) / (k_[i + 1] - k_[i]);
if (q1 <= q2)
return true;
return false;
}
}
|
