org.jquantlib.math.statistics

Class GenericGaussianStatistics

java.lang.Object

org.jquantlib.math.statistics.GeneralStatistics

org.jquantlib.math.statistics.GenericGaussianStatistics

Direct Known Subclasses:

GaussianStatistics

public abstract class GenericGaussianStatistics
extends GeneralStatistics

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.

Constructor Summary

Constructors

Constructor and Description
GenericGaussianStatistics()

Method Summary

Modifier and Type	Method and Description
double	gaussianAverageShortfall(double target) gaussian-assumption Average Shortfall (averaged shortfallness)
double	gaussianDownsideDeviation() returns the downside deviation, defined as the square root of the downside variance.
double	gaussianDownsideVariance() returns the downside variance, defined as
double	gaussianExpectedShortfall(double percentile) gaussian-assumption Expected Shortfall at a given percentile
double	gaussianPercentile(double percentile)
double	gaussianPotentialUpside(double percentile) percentile must be in range [90%-100%)
double	gaussianRegret(double target) returns the variance of observations below target
double	gaussianShortfall(double target) gaussian-assumption Shortfall (observations below target)
double	gaussianTopPercentile(double percentile) percentile must be in range (0%-100%) extremes excluded
double	gaussianValueAtRisk(double percentile) percentile must be in range [90%-100%)

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

GenericGaussianStatistics

public GenericGaussianStatistics()

Method Detail

gaussianDownsideVariance

public double gaussianDownsideVariance()

returns the downside variance, defined as

,

where = 0 if x > 0 and = 1 if x <0

gaussianDownsideDeviation

public double gaussianDownsideDeviation()

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

gaussianRegret

public double gaussianRegret(double target)

returns the variance of observations below target

See Also:

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

gaussianPercentile

public double gaussianPercentile(double percentile)

gaussianTopPercentile

public double gaussianTopPercentile(double percentile)

percentile must be in range (0%-100%) extremes excluded

gaussianPotentialUpside

public double gaussianPotentialUpside(double percentile)

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

gaussianValueAtRisk

public double gaussianValueAtRisk(double percentile)

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

gaussianExpectedShortfall

public double gaussianExpectedShortfall(double percentile)

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,

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

See Also:

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

gaussianShortfall

public double gaussianShortfall(double target)

gaussian-assumption Shortfall (observations below target)

gaussianAverageShortfall

public double gaussianAverageShortfall(double target)

gaussian-assumption Average Shortfall (averaged shortfallness)