GenericRiskStatistics< S > Class Template Reference

empirical-distribution risk measures More...

#include <ql/math/statistics/riskstatistics.hpp>

Inherits S.

Public Types
typedef S::value_type	value_type

Public Member Functions
Real	semiVariance () const
Real	semiDeviation () const
Real	downsideVariance () const
Real	downsideDeviation () const
Real	regret (Real target) const
Real	potentialUpside (Real percentile) const
	potential upside (the reciprocal of VAR) at a given percentile More...
Real	valueAtRisk (Real percentile) const
	value-at-risk at a given percentile More...
Real	expectedShortfall (Real percentile) const
	expected shortfall at a given percentile More...
Real	shortfall (Real target) const
Real	averageShortfall (Real target) const

Detailed Description

template<class S>
class QuantLib::GenericRiskStatistics< S >

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.

Examples

DiscreteHedging.cpp, and MarketModels.cpp.

Member Function Documentation

semiVariance()

Real semiVariance

returns the variance of observations below the mean,

\[ \frac{N}{N-1} \mathrm{E}\left[ (x-\langle x \rangle)^2 \;|\; x < \langle x \rangle \right]. \]

See Markowitz (1959).

semiDeviation()

Real semiDeviation

returns the semi deviation, defined as the square root of the semi variance.

downsideVariance()

Real downsideVariance

returns the variance of observations below 0.0,

\[ \frac{N}{N-1} \mathrm{E}\left[ x^2 \;|\; x < 0\right]. \]

downsideDeviation()

Real downsideDeviation

returns the downside deviation, defined as the square root of the downside variance.

regret()

Real regret

(

Real

target

)

const

returns the variance of observations below target,

\[ \frac{N}{N-1} \mathrm{E}\left[ (x-t)^2 \;|\; x < t \right]. \]

See Dembo and Freeman, "The Rules Of Risk", Wiley (2001).

potentialUpside()

Real potentialUpside

(

Real

centile

)

const

potential upside (the reciprocal of VAR) at a given percentile

Precondition

percentile must be in range [90%-100%)

valueAtRisk()

Real valueAtRisk

(

Real

centile

)

const

value-at-risk at a given percentile

Precondition

percentile must be in range [90%-100%)

expectedShortfall()

Real expectedShortfall

(

Real

centile

)

const

expected shortfall at a given percentile

returns the expected loss in case that the loss exceeded a VaR threshold,

\[ \mathrm{E}\left[ x \;|\; x < \mathrm{VaR}(p) \right], \]

that is the average of observations below the given percentile \( p \). Also know as conditional value-at-risk.

See Artzner, Delbaen, Eber and Heath, "Coherent measures of risk", Mathematical Finance 9 (1999)

Precondition

percentile must be in range [90%-100%)

shortfall()

Real shortfall

(

Real

target

)

const

probability of missing the given target, defined as

\[ \mathrm{E}\left[ \Theta \;|\; (-\infty,\infty) \right] \]

where

\[ \Theta(x) = \left\{ \begin{array}{ll} 1 & x < t \\ 0 & x \geq t \end{array} \right. \]

averageShortfall()

Real averageShortfall

(

Real

target

)

const

averaged shortfallness, defined as

\[ \mathrm{E}\left[ t-x \;|\; x<t \right] \]