org.jquantlib.math.statistics

Class GenericRiskStatistics

java.lang.Object

org.jquantlib.math.statistics.GeneralStatistics

org.jquantlib.math.statistics.GenericGaussianStatistics

org.jquantlib.math.statistics.GaussianStatistics

org.jquantlib.math.statistics.GenericRiskStatistics

Direct Known Subclasses:

IncrementalStatistics, RiskStatistics

public class GenericRiskStatistics
extends GaussianStatistics

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.

Constructor Summary

Constructors

Constructor and Description
GenericRiskStatistics()

Method Summary

Modifier and Type	Method and Description
double	averageShortfall(double target) averaged shortfallness, defined as
double	downsideDeviation() returns the downside deviation, defined as the square root of the downside variance.
double	downsideVariance() returns the variance of observations below 0.0, \frac{N}{N-1} \mathrm{E}\left[ x^2 \;|\; x < 0\right].
double	expectedShortfall(double centile) expected shortfall at a given percentile
double	potentialUpside(double centile) potential upside (the reciprocal of VaR) at a given percentile
double	regret(double target) returns the variance of observations below target, \frac{N}{N-1} \mathrm{E}\left[ (x-t)^2 \;|\; x < t \right].
double	semiDeviation() returns the semi deviation, defined as the square root of the semi variance.
double	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].
double	shortfall(double target) probability of missing the given target, defined as where \Theta(x) = \left\{ \begin{array}{ll} 1 & x < t \\ 0 & x \geq t \end{array} \right.
double	valueAtRisk(double centile) value-at-risk at a given percentile

Methods inherited from class org.jquantlib.math.statistics.GenericGaussianStatistics

gaussianAverageShortfall, gaussianDownsideDeviation, gaussianDownsideVariance, gaussianExpectedShortfall, gaussianPercentile, gaussianPotentialUpside, gaussianRegret, gaussianShortfall, gaussianTopPercentile, gaussianValueAtRisk

Methods inherited from class org.jquantlib.math.statistics.GeneralStatistics

add, add, addSequence, addSequence, addSequence, addSequence, data, errorEstimate, expectationValue, kurtosis, max, mean, min, percentile, reset, samples, skewness, sort, standardDeviation, topPercentile, variance, weightSum

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GenericRiskStatistics

public GenericRiskStatistics()

Method Detail

semiVariance

public double semiVariance()

returns the variance of observations below the mean,

See Also:

(1959).

semiDeviation

public double semiDeviation()

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

downsideVariance

public double downsideVariance()

returns the variance of observations below 0.0,

downsideDeviation

public double downsideDeviation()

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

regret

public double regret(double target)

returns the variance of observations below target,

See Also:

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

potentialUpside

public double potentialUpside(double centile)

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

valueAtRisk

public double valueAtRisk(double centile)

value-at-risk at a given percentile

expectedShortfall

public double expectedShortfall(double centile)

expected shortfall at a given percentile

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

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

See Also:

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

shortfall

public double shortfall(double target)

probability of missing the given target, defined as where \Theta(x) = \left\{ \begin{array}{ll} 1 & x < t \\ 0 & x \geq t \end{array} \right. }

averageShortfall

public double averageShortfall(double target)

averaged shortfallness, defined as