/usr/include/ql/math/statistics/gaussianstatistics.hpp is in libquantlib0-dev 1.9.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 Ferdinando Ametrano
Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
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.
*/
/*! \file gaussianstatistics.hpp
\brief statistics tool for gaussian-assumption risk measures
*/
#ifndef quantlib_gaussian_statistics_h
#define quantlib_gaussian_statistics_h
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/statistics/generalstatistics.hpp>
namespace QuantLib {
//! Statistics tool for gaussian-assumption risk measures
/*! This class wraps a somewhat generic statistic tool and adds
a number of gaussian risk measures (e.g.: value-at-risk, expected
shortfall, etc.) based on the mean and variance provided by
the underlying statistic tool.
*/
template<class Stat>
class GenericGaussianStatistics : public Stat {
public:
typedef typename Stat::value_type value_type;
GenericGaussianStatistics() {}
GenericGaussianStatistics(const Stat& s) : Stat(s) {}
//! \name Gaussian risk measures
//@{
/*! returns the downside variance, defined as
\f[ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N}
\theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} \f],
where \f$ \theta \f$ = 0 if x > 0 and
\f$ \theta \f$ =1 if x <0
*/
Real gaussianDownsideVariance() const {
return gaussianRegret(0.0);
}
/*! returns the downside deviation, defined as the
square root of the downside variance.
*/
Real gaussianDownsideDeviation() const {
return std::sqrt(gaussianDownsideVariance());
}
/*! returns the variance of observations below target
\f[ \frac{\sum w_i (min(0, x_i-target))^2 }{\sum w_i}. \f]
See Dembo, Freeman "The Rules Of Risk", Wiley (2001)
*/
Real gaussianRegret(Real target) const;
/*! gaussian-assumption y-th percentile, defined as the value x
such that \f[ y = \frac{1}{\sqrt{2 \pi}}
\int_{-\infty}^{x} \exp (-u^2/2) du \f]
*/
Real gaussianPercentile(Real percentile) const;
Real gaussianTopPercentile(Real percentile) const;
//! gaussian-assumption Potential-Upside at a given percentile
Real gaussianPotentialUpside(Real percentile) const;
//! gaussian-assumption Value-At-Risk at a given percentile
Real gaussianValueAtRisk(Real percentile) const;
//! gaussian-assumption Expected Shortfall at a given percentile
/*! Assuming a gaussian distribution it
returns the expected loss in case that the loss exceeded
a VaR threshold,
\f[ \mathrm{E}\left[ x \;|\; x < \mathrm{VaR}(p) \right], \f]
that is the average of observations below the
given percentile \f$ p \f$.
Also know as conditional value-at-risk.
See Artzner, Delbaen, Eber and Heath,
"Coherent measures of risk", Mathematical Finance 9 (1999)
*/
Real gaussianExpectedShortfall(Real percentile) const;
//! gaussian-assumption Shortfall (observations below target)
Real gaussianShortfall(Real target) const;
//! gaussian-assumption Average Shortfall (averaged shortfallness)
Real gaussianAverageShortfall(Real target) const;
//@}
};
//! default gaussian statistic tool
typedef GenericGaussianStatistics<GeneralStatistics> GaussianStatistics;
//! Helper class for precomputed distributions
class StatsHolder {
public:
typedef Real value_type;
StatsHolder(Real mean,
Real standardDeviation)
: mean_(mean), standardDeviation_(standardDeviation) {}
~StatsHolder() {}
Real mean() const { return mean_; }
Real standardDeviation() const { return standardDeviation_; }
private:
Real mean_, standardDeviation_;
};
// inline definitions
template<class Stat>
inline
Real GenericGaussianStatistics<Stat>::gaussianRegret(Real target) const {
Real m = this->mean();
Real std = this->standardDeviation();
Real variance = std*std;
CumulativeNormalDistribution gIntegral(m, std);
NormalDistribution g(m, std);
Real firstTerm = variance + m*m - 2.0*target*m + target*target;
Real alfa = gIntegral(target);
Real secondTerm = m - target;
Real beta = variance*g(target);
Real result = alfa*firstTerm - beta*secondTerm;
return result/alfa;
}
/*! \pre percentile must be in range (0%-100%) extremes excluded */
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianPercentile(
Real percentile) const {
QL_REQUIRE(percentile>0.0,
"percentile (" << percentile << ") must be > 0.0");
QL_REQUIRE(percentile<1.0,
"percentile (" << percentile << ") must be < 1.0");
InverseCumulativeNormal gInverse(Stat::mean(),
Stat::standardDeviation());
return gInverse(percentile);
}
/*! \pre percentile must be in range (0%-100%) extremes excluded */
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianTopPercentile(
Real percentile) const {
return gaussianPercentile(1.0-percentile);
}
/*! \pre percentile must be in range [90%-100%) */
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianPotentialUpside(
Real percentile) const {
QL_REQUIRE(percentile<1.0 && percentile>=0.9,
"percentile (" << percentile << ") out of range [0.9, 1)");
Real result = gaussianPercentile(percentile);
// potential upside must be a gain, i.e., floored at 0.0
return std::max<Real>(result, 0.0);
}
/*! \pre percentile must be in range [90%-100%) */
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianValueAtRisk(
Real percentile) const {
QL_REQUIRE(percentile<1.0 && percentile>=0.9,
"percentile (" << percentile << ") out of range [0.9, 1)");
Real result = gaussianPercentile(1.0-percentile);
// VAR must be a loss
// this means that it has to be MIN(dist(1.0-percentile), 0.0)
// VAR must also be a positive quantity, so -MIN(*)
return -std::min<Real>(result, 0.0);
}
/*! \pre percentile must be in range [90%-100%) */
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianExpectedShortfall(
Real percentile) const {
QL_REQUIRE(percentile<1.0 && percentile>=0.9,
"percentile (" << percentile << ") out of range [0.9, 1)");
Real m = this->mean();
Real std = this->standardDeviation();
InverseCumulativeNormal gInverse(m, std);
Real var = gInverse(1.0-percentile);
NormalDistribution g(m, std);
Real result = m - std*std*g(var)/(1.0-percentile);
// expectedShortfall must be a loss
// this means that it has to be MIN(result, 0.0)
// expectedShortfall must also be a positive quantity, so -MIN(*)
return -std::min<Real>(result, 0.0);
}
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianShortfall(
Real target) const {
CumulativeNormalDistribution gIntegral(this->mean(),
this->standardDeviation());
return gIntegral(target);
}
template<class Stat>
inline Real GenericGaussianStatistics<Stat>::gaussianAverageShortfall(
Real target) const {
Real m = this->mean();
Real std = this->standardDeviation();
CumulativeNormalDistribution gIntegral(m, std);
NormalDistribution g(m, std);
return ( (target-m) + std*std*g(target)/gIntegral(target) );
}
}
#endif
|