1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2014 Jose Aparicio
5
6 This file is part of QuantLib, a free-software/open-source library
7 for financial quantitative analysts and developers - http://quantlib.org/
8
9 QuantLib is free software: you can redistribute it and/or modify it
10 under the terms of the QuantLib license. You should have received a
11 copy of the license along with this program; if not, please email
12 <quantlib-dev@lists.sf.net>. The license is also available online at
13 <http://quantlib.org/license.shtml>.
14
15 This program is distributed in the hope that it will be useful, but WITHOUT
16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17 FOR A PARTICULAR PURPOSE. See the license for more details.
18*/
19
20#include <ql/experimental/math/tcopulapolicy.hpp>
21#include <numeric>
22#include <algorithm>
23
24namespace QuantLib {
25
26 TCopulaPolicy::TCopulaPolicy(
27 const std::vector<std::vector<Real> >& factorWeights,
28 const initTraits& vals)
29 {
30 for (int tOrder : vals.tOrders) {
31 // require no T is of order 2 (finite variance)
32 QL_REQUIRE(tOrder > 2, "Non finite variance T in latent model.");
33
34 distributions_.emplace_back(args&: tOrder);
35 // inverses T variaces used in normalization of the random factors
36 // For low values of the T order this number is very close to zero
37 // and it enters the expressions dividing them, which introduces
38 // numerical errors.
39 varianceFactors_.push_back(x: std::sqrt(x: (tOrder - 2.) / tOrder));
40 }
41
42 for (const auto& factorWeight : factorWeights) {
43 // This ensures the latent model is 'canonical'
44 QL_REQUIRE(vals.tOrders.size() == factorWeight.size() + 1,
45 // num factors plus one
46 "Incompatible number of T functions and number of factors.");
47
48 Real factorsNorm = std::inner_product(first1: factorWeight.begin(), last1: factorWeight.end(),
49 first2: factorWeight.begin(), init: Real(0.));
50 QL_REQUIRE(factorsNorm < 1.,
51 "Non normal random factor combination.");
52 Real idiosyncFctr = std::sqrt(x: 1.-factorsNorm);
53
54 // linear comb factors ajusted for the variance renormalization:
55 std::vector<Real> normFactorWeights;
56 for (Size iFactor = 0; iFactor < factorWeight.size(); iFactor++)
57 normFactorWeights.push_back(x: factorWeight[iFactor] * varianceFactors_[iFactor]);
58 // idiosincratic term, all Z factors are assumed identical.
59 normFactorWeights.push_back(x: idiosyncFctr * varianceFactors_.back());
60 latentVarsCumul_.emplace_back(args: vals.tOrders, args&: normFactorWeights);
61 latentVarsInverters_.emplace_back(args: vals.tOrders, args&: normFactorWeights);
62 }
63 }
64
65 std::vector<Real> TCopulaPolicy::allFactorCumulInverter(
66 const std::vector<Real>& probs) const
67 {
68 #if defined(QL_EXTRA_SAFETY_CHECKS)
69 QL_REQUIRE(probs.size()-latentVarsCumul_.size()
70 == distributions_.size()-1,
71 "Incompatible sample and latent model sizes");
72 #endif
73
74 std::vector<Real> result(probs.size());
75 Size indexSystemic = 0;
76 std::transform(first: probs.begin(), last: probs.begin() + varianceFactors_.size()-1,
77 result: result.begin(),
78 unary_op: [&](Probability p) { return inverseCumulativeDensity(p, iFactor: indexSystemic++); });
79 std::transform(first: probs.begin() + varianceFactors_.size()-1, last: probs.end(),
80 result: result.begin()+ varianceFactors_.size()-1,
81 unary_op: [&](Probability p) { return inverseCumulativeZ(p); });
82 return result;
83 }
84
85}
86

source code of quantlib/ql/experimental/math/tcopulapolicy.cpp