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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2016 Klaus Spanderen
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 normalclvmodel.cpp
*/
#include <ql/exercise.hpp>
#include <ql/experimental/models/normalclvmodel.hpp>
#include <ql/instruments/vanillaoption.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/integrals/gaussianquadratures.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/solvers1d/brent.hpp>
#include <ql/methods/finitedifferences/utilities/gbsmrndcalculator.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/processes/ornsteinuhlenbeckprocess.hpp>
#include <utility>
namespace QuantLib {
NormalCLVModel::NormalCLVModel(const ext::shared_ptr<GeneralizedBlackScholesProcess>& bsProcess,
ext::shared_ptr<OrnsteinUhlenbeckProcess> ouProcess,
const std::vector<Date>& maturityDates,
Size lagrangeOrder,
Real pMax,
Real pMin)
: x_(M_SQRT2 * GaussHermiteIntegration(lagrangeOrder).x()),
sigma_((pMax != Null<Real>()) ?
x_.back() / InverseCumulativeNormal()(pMax) :
(pMin != Null<Real>()) ? x_.front() / InverseCumulativeNormal()(pMin) : Real(1.0)),
bsProcess_(bsProcess), ouProcess_(std::move(ouProcess)), maturityDates_(maturityDates),
rndCalculator_(ext::make_shared<GBSMRNDCalculator>(bsProcess)),
maturityTimes_(maturityDates.size()) {
registerWith(bsProcess_);
registerWith(ouProcess_);
for (Size i=0; i < maturityTimes_.size(); ++i) {
maturityTimes_[i] = bsProcess_->time(maturityDates[i]);
QL_REQUIRE(i==0 || maturityTimes_[i-1] < maturityTimes_[i],
"dates must be sorted");
}
}
Real NormalCLVModel::cdf(const Date& d, Real k) const {
return rndCalculator_->cdf(k, bsProcess_->time(d));
}
Real NormalCLVModel::invCDF(const Date& d, Real q) const {
return rndCalculator_->invcdf(q, bsProcess_->time(d));
}
Array NormalCLVModel::collocationPointsX(const Date& d) const {
const Time t = bsProcess_->time(d);
const Real expectation
= ouProcess_->expectation(0.0, ouProcess_->x0(), t);
const Real stdDeviation
= ouProcess_->stdDeviation(0.0, ouProcess_->x0(), t);
return expectation + stdDeviation*x_;
}
Array NormalCLVModel::collocationPointsY(const Date& d) const {
Array s(x_.size());
CumulativeNormalDistribution N;
for (Size i=0, n=s.size(); i < n; ++i) {
s[i] = invCDF(d, N(x_[i]/sigma_));
}
return s;
}
std::function<Real(Time, Real)> NormalCLVModel::g() const {
calculate();
return g_;
}
NormalCLVModel::MappingFunction::MappingFunction(
const NormalCLVModel& model)
: y_(model.x_.size()),
sigma_(model.sigma_),
ouProcess_(model.ouProcess_),
data_(ext::make_shared<InterpolationData>(model)) {
for (Size i=0; i < data_->s_.columns(); ++i) {
const Array y = model.collocationPointsY(model.maturityDates_[i]);
std::copy(y.begin(), y.end(), data_->s_.column_begin(i));
}
for (Size i=0; i < data_->s_.rows(); ++i) {
data_->interpl_.emplace_back(data_->t_.begin(), data_->t_.end(),
data_->s_.row_begin(i));
}
}
Real NormalCLVModel::MappingFunction::operator()(Time t, Real x) const {
for (Size i=0; i < y_.size(); ++i) {
y_[i] = data_->interpl_[i](t, true);
}
const Real expectation
= ouProcess_->expectation(0.0, ouProcess_->x0(), t);
const Real stdDeviation
= ouProcess_->stdDeviation(0.0, ouProcess_->x0(), t);
const Real r = sigma_*(x-expectation)/stdDeviation;
return data_->lagrangeInterpl_.value(y_, r);
}
void NormalCLVModel::performCalculations() const {
g_ = std::function<Real(Time, Real)>(MappingFunction(*this));
}
}
|
