/usr/include/ql/math/statistics/riskstatistics.hpp is in libquantlib0-dev 1.1-2build1.
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 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 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 riskstatistics.hpp
\brief empirical-distribution risk measures
*/
#ifndef quantlib_risk_statistics_h
#define quantlib_risk_statistics_h
#include <ql/math/functional.hpp>
#include <ql/math/statistics/gaussianstatistics.hpp>
namespace QuantLib {
//! empirical-distribution risk measures
/*! This class wraps a somewhat generic statistic tool and adds
a number of risk measures (e.g.: value-at-risk, expected
shortfall, etc.) based on the data distribution as reported by
the underlying statistic tool.
\todo add historical annualized volatility
*/
template <class S>
class GenericRiskStatistics : public S {
public:
typedef typename S::value_type value_type;
/*! returns the variance of observations below the mean,
\f[ \frac{N}{N-1}
\mathrm{E}\left[ (x-\langle x \rangle)^2 \;|\;
x < \langle x \rangle \right]. \f]
See Markowitz (1959).
*/
Real semiVariance() const;
/*! returns the semi deviation, defined as the
square root of the semi variance.
*/
Real semiDeviation() const;
/*! returns the variance of observations below 0.0,
\f[ \frac{N}{N-1}
\mathrm{E}\left[ x^2 \;|\; x < 0\right]. \f]
*/
Real downsideVariance() const;
/*! returns the downside deviation, defined as the
square root of the downside variance.
*/
Real downsideDeviation() const;
/*! returns the variance of observations below target,
\f[ \frac{N}{N-1}
\mathrm{E}\left[ (x-t)^2 \;|\;
x < t \right]. \f]
See Dembo and Freeman, "The Rules Of Risk", Wiley (2001).
*/
Real regret(Real target) const;
//! potential upside (the reciprocal of VAR) at a given percentile
Real potentialUpside(Real percentile) const;
//! value-at-risk at a given percentile
Real valueAtRisk(Real percentile) const;
//! expected shortfall at a given percentile
/*! 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 expectedShortfall(Real percentile) const;
/*! probability of missing the given target, defined as
\f[ \mathrm{E}\left[ \Theta \;|\; (-\infty,\infty) \right] \f]
where
\f[ \Theta(x) = \left\{
\begin{array}{ll}
1 & x < t \\
0 & x \geq t
\end{array}
\right. \f]
*/
Real shortfall(Real target) const;
/*! averaged shortfallness, defined as
\f[ \mathrm{E}\left[ t-x \;|\; x<t \right] \f]
*/
Real averageShortfall(Real target) const;
};
//! default risk measures tool
/*! \test the correctness of the returned values is tested by
checking them against numerical calculations.
*/
typedef GenericRiskStatistics<GaussianStatistics> RiskStatistics;
// inline definitions
template <class S>
inline Real GenericRiskStatistics<S>::semiVariance() const {
return regret(this->mean());
}
template <class S>
inline Real GenericRiskStatistics<S>::semiDeviation() const {
return std::sqrt(semiVariance());
}
template <class S>
inline Real GenericRiskStatistics<S>::downsideVariance() const {
return regret(0.0);
}
template <class S>
inline Real GenericRiskStatistics<S>::downsideDeviation() const {
return std::sqrt(downsideVariance());
}
// template definitions
template <class S>
Real GenericRiskStatistics<S>::regret(Real target) const {
// average over the range below the target
std::pair<Real,Size> result =
this->expectationValue(compose(square<Real>(),
std::bind2nd(std::minus<Real>(),
target)),
std::bind2nd(std::less<Real>(), target));
Real x = result.first;
Size N = result.second;
QL_REQUIRE(N > 1,
"samples under target <= 1, unsufficient");
return (N/(N-1.0))*x;
}
/*! \pre percentile must be in range [90%-100%) */
template <class S>
Real GenericRiskStatistics<S>::potentialUpside(Real centile)
const {
QL_REQUIRE(centile>=0.9 && centile<1.0,
"percentile (" << centile << ") out of range [0.9, 1.0)");
// potential upside must be a gain, i.e., floored at 0.0
return std::max<Real>(this->percentile(centile), 0.0);
}
/*! \pre percentile must be in range [90%-100%) */
template <class S>
Real GenericRiskStatistics<S>::valueAtRisk(Real centile) const {
QL_REQUIRE(centile>=0.9 && centile<1.0,
"percentile (" << centile << ") out of range [0.9, 1.0)");
// must be a loss, i.e., capped at 0.0 and negated
return -std::min<Real>(this->percentile(1.0-centile), 0.0);
}
/*! \pre percentile must be in range [90%-100%) */
template <class S>
Real GenericRiskStatistics<S>::expectedShortfall(Real centile) const {
QL_REQUIRE(centile>=0.9 && centile<1.0,
"percentile (" << centile << ") out of range [0.9, 1.0)");
QL_ENSURE(this->samples() != 0, "empty sample set");
Real target = -valueAtRisk(centile);
std::pair<Real,Size> result =
this->expectationValue(identity<Real>(),
std::bind2nd(std::less<Real>(),
target));
Real x = result.first;
Size N = result.second;
QL_ENSURE(N != 0, "no data below the target");
// must be a loss, i.e., capped at 0.0 and negated
return -std::min<Real>(x, 0.0);
}
template <class S>
Real GenericRiskStatistics<S>::shortfall(Real target) const {
QL_ENSURE(this->samples() != 0, "empty sample set");
return this->expectationValue(clip(constant<Real,Real>(1.0),
std::bind2nd(std::less<Real>(),
target)),
everywhere()).first;
}
template <class S>
Real GenericRiskStatistics<S>::averageShortfall(Real target)
const {
std::pair<Real,Size> result =
this->expectationValue(std::bind1st(std::minus<Real>(),
target),
std::bind2nd(std::less<Real>(),
target));
Real x = result.first;
Size N = result.second;
QL_ENSURE(N != 0, "no data below the target");
return x;
}
}
#endif
|