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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Jose Aparicio
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.
*/
#ifndef quantlib_gaussian_copula_policy_hpp
#define quantlib_gaussian_copula_policy_hpp
#include <ql/math/distributions/normaldistribution.hpp>
#include <vector>
#include <numeric>
#include <algorithm>
namespace QuantLib {
/*! Gaussian Latent Model's copula policy. Its simplicity is a result of
the convolution stability of the Gaussian distribution.
*/
/* This is the only case that would have allowed the policy to be static,
but other copulas will need parameters and initialization.*/
struct GaussianCopulaPolicy {
typedef int initTraits;
explicit GaussianCopulaPolicy(
const std::vector<std::vector<Real> >& factorWeights =
std::vector<std::vector<Real> >(),
const initTraits& dummy = int())
: numFactors_(factorWeights.size() + factorWeights[0].size())
{
/* check factors in LM are normalized. */
for (const auto& factorWeight : factorWeights) {
Real factorsNorm = std::inner_product(factorWeight.begin(), factorWeight.end(),
factorWeight.begin(), Real(0.));
QL_REQUIRE(factorsNorm < 1.,
"Non normal random factor combination.");
}
/* check factor matrix is squared .......... */
}
/*! Number of independent random factors.
This is the only methos that ould stop the class from being static, it
is needed for the MC generator construction.
*/
Size numFactors() const {
return numFactors_;
}
//! returns a copy of the initialization arguments
initTraits getInitTraits() const {
return initTraits();
}
/*! Cumulative probability of a given latent variable
The iVariable parameter is the index of the requested variable.
*/
Probability cumulativeY(Real val, Size iVariable) const {
return cumulative_(val);
}
//! Cumulative probability of the idiosyncratic factors (all the same)
Probability cumulativeZ(Real z) const {
return cumulative_(z);
}
/*! Probability density of a given realization of values of the systemic
factors (remember they are independent). In the normal case, since
they all follow the same law it is just a trivial product of the same
density.
Intended to be used in numerical integration of an arbitrary function
depending on those values.
*/
Probability density(const std::vector<Real>& m) const {
return std::accumulate(m.begin(), m.end(), Real(1.),
[&](Real x, Real y) -> Real { return x*density_(y); });
}
/*! Returns the inverse of the cumulative distribution of the (modelled)
latent variable (as indexed by iVariable). The normal stability avoids
the convolution of the factors' distributions
*/
Real inverseCumulativeY(Probability p, Size iVariable) const {
return InverseCumulativeNormal::standard_value(p);
}
/*! Returns the inverse of the cumulative distribution of the
idiosyncratic factor (identically distributed for all latent variables)
*/
Real inverseCumulativeZ(Probability p) const {
return InverseCumulativeNormal::standard_value(p);
}
/*! Returns the inverse of the cumulative distribution of the
systemic factor iFactor.
*/
Real inverseCumulativeDensity(Probability p, Size iFactor) const {
return InverseCumulativeNormal::standard_value(p);
}
//!
//to use this (by default) version, the generator must be a uniform one.
std::vector<Real> allFactorCumulInverter(const std::vector<Real>& probs) const {
std::vector<Real> result;
result.resize(probs.size());
std::transform(probs.begin(), probs.end(), result.begin(),
[&](Real p){ return InverseCumulativeNormal::standard_value(p); });
return result;
}
private:
mutable Size numFactors_;
// no op =
static const NormalDistribution density_;
static const CumulativeNormalDistribution cumulative_;
};
}
#endif
|
