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/*
Copyright (C) 2000, 2001, 2002 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 ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
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 riskmeasures.hpp
\brief Risk functions
\fullpath
ql/Math/%riskmeasures.hpp
*/
// $Id: riskmeasures.hpp,v 1.5 2002/01/16 14:42:29 nando Exp $
#ifndef quantlib_risk_measures_h
#define quantlib_risk_measures_h
#include <ql/null.hpp>
#include <ql/Math/normaldistribution.hpp>
#include <iostream>
#include <vector>
namespace QuantLib {
namespace Math {
//! Interface for risk functions
class RiskMeasures {
public:
RiskMeasures() {}
double potentialUpside(double percentile,
double mean,
double std) const ;
double valueAtRisk(double percentile,
double mean,
double std) const ;
double expectedShortfall(double percentile,
double mean,
double std) const ;
double shortfall(double target,
double mean,
double std) const ;
double averageShortfall(double target,
double mean,
double std) const ;
};
// inline definitions
/*! \pre percentile must be in range 90%-100% */
inline double RiskMeasures::potentialUpside(double percentile,
double mean,
double std) const {
QL_REQUIRE(percentile<1.0 && percentile>=0.9,
"RiskMeasures::potentialUpside : percentile (" +
DoubleFormatter::toString(percentile) +
") out of range 90%-100%");
Math::InvCumulativeNormalDistribution gInverse(mean, std);
// PotenzialUpSide must be a gain
// this means that it has to be MAX(dist(percentile), 0.0)
return QL_MAX(gInverse(percentile), 0.0);
}
/*! \pre percentile must be in range 90%-100% */
inline double RiskMeasures::valueAtRisk(double percentile,
double mean,
double std) const {
QL_REQUIRE(percentile<1.0 && percentile>=0.9,
"RiskMeasures::valueAtRisk : percentile (" +
DoubleFormatter::toString(percentile) +
") out of range 90%-100%");
Math::InvCumulativeNormalDistribution gInverse(mean, std);
// 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 -QL_MIN(gInverse(1.0-percentile), 0.0);
}
/*! \pre percentile must be in range 90%-100% */
inline double RiskMeasures::expectedShortfall(double percentile,
double mean,
double std) const {
QL_REQUIRE(percentile<1.0 && percentile>=0.9,
"RiskMeasures::expectedShortfall : percentile (" +
DoubleFormatter::toString(percentile) +
") out of range 90%-100%");
Math::InvCumulativeNormalDistribution gInverse(mean, std);
double var = gInverse(1.0-percentile);
Math::NormalDistribution g(mean, std);
double result = mean - 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 -QL_MIN(result, 0.0);
}
inline double RiskMeasures::shortfall(double target,
double mean,
double std) const {
Math::CumulativeNormalDistribution gIntegral(mean, std);
return gIntegral(target);
}
inline double RiskMeasures::averageShortfall(double target,
double mean,
double std) const {
Math::CumulativeNormalDistribution gIntegral(mean, std);
Math::NormalDistribution g(mean, std);
return ( (target-mean)*gIntegral(target) + std*std*g(target) );
}
}
}
#endif
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