Class RiskStatisticsExtensions

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The empirical risk measures (semi-variance, regret, value-at-risk, expected shortfall, …), from the samples of a statistics tool that keeps them: QuantLib's GenericRiskStatistics<S>, which derives from its type parameter, as C# 14 extension members over any IEmpiricalStatistics.

public static class RiskStatisticsExtensions

Inheritance

object

RiskStatisticsExtensions

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

QuantLib's RiskStatistics, GenericRiskStatistics<GaussianStatistics>, and its Statistics typedef are GeneralStatistics with these members and those of GaussianStatisticsExtensions.

ExpectedShortfall<TStat>(TStat, double) where no sample lies below the value-at-risk's level reads the level itself, 0 with no loss and the value-at-risk where the tail is an atom at that level, where QuantLib refuses "no data below the target": a documented divergence.

Methods

AverageShortfall<TStat>(TStat, double)

The averaged shortfallness, E[t − x | x < t].

public static double AverageShortfall<TStat>(this TStat stats, double target) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

target double

The target.

Returns

double

The average shortfall.

Type Parameters

TStat

Exceptions

NanoQLException

No sample lies below the target.

DownsideDeviation<TStat>(TStat)

The downside deviation, the square root of the downside variance.

public static double DownsideDeviation<TStat>(this TStat stats) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

Returns

double

The downside deviation.

Type Parameters

TStat

Exceptions

NanoQLException

There are fewer than two negative samples.

DownsideVariance<TStat>(TStat)

The variance of observations below 0, N/(N − 1) E[x² | x < 0].

public static double DownsideVariance<TStat>(this TStat stats) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

Returns

double

The downside variance.

Type Parameters

TStat

Exceptions

NanoQLException

There are fewer than two negative samples.

ExpectedShortfall<TStat>(TStat, double)

The expected shortfall at a percentile: the expected loss where the loss exceeds the value-at-risk, E[x | x < VaR(p)], the average of observations below the percentile, also known as conditional value-at-risk (Artzner, Delbaen, Eber and Heath, "Coherent measures of risk", Mathematical Finance 9, 1999); capped at 0 and negated.

public static double ExpectedShortfall<TStat>(this TStat stats, double percentile) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

percentile double

The percentile, in [0.9, 1).

Returns

double

The expected shortfall; where no sample lies below the value-at-risk's level, that level capped and negated: 0 with no loss, the value-at-risk where the tail is an atom at that level (a divergence: QuantLib refuses).

Type Parameters

TStat

Exceptions

ArgumentOutOfRangeException

percentile is outside [0.9, 1).

NanoQLException

There's no sample.

PotentialUpside<TStat>(TStat, double)

The potential upside (the reciprocal of value-at-risk) at a percentile, floored at 0.

public static double PotentialUpside<TStat>(this TStat stats, double percentile) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

percentile double

The percentile, in [0.9, 1).

Returns

double

The potential upside.

Type Parameters

TStat

Exceptions

ArgumentOutOfRangeException

percentile is outside [0.9, 1).

Regret<TStat>(TStat, double)

The variance of observations below a target, N/(N − 1) E[(x − t)² | x < t] (Dembo and Freeman, "The Rules Of Risk", Wiley, 2001).

public static double Regret<TStat>(this TStat stats, double target) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

target double

The target.

Returns

double

The regret.

Type Parameters

TStat

Exceptions

NanoQLException

There are fewer than two samples below the target.

SemiDeviation<TStat>(TStat)

The semi-deviation, the square root of the semi-variance.

public static double SemiDeviation<TStat>(this TStat stats) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

Returns

double

The semi-deviation.

Type Parameters

TStat

Exceptions

NanoQLException

There are fewer than two samples below the mean.

SemiVariance<TStat>(TStat)

The variance of observations below the mean, N/(N − 1) E[(x − ⟨x⟩)² | x < ⟨x⟩] (Markowitz, 1959).

public static double SemiVariance<TStat>(this TStat stats) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

Returns

double

The semi-variance.

Type Parameters

TStat

Exceptions

NanoQLException

There are fewer than two samples below the mean.

Shortfall<TStat>(TStat, double)

The probability of missing a target, E[Θ | (−∞, ∞)], where Θ(x) is 1 for x < t and 0 for x ≥ t.

public static double Shortfall<TStat>(this TStat stats, double target) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

target double

The target.

Returns

double

The shortfall.

Type Parameters

TStat

Exceptions

NanoQLException

There's no sample.

ValueAtRisk<TStat>(TStat, double)

The value-at-risk at a percentile: the (1 − percentile)-th percentile, capped at 0 and negated.

public static double ValueAtRisk<TStat>(this TStat stats, double percentile) where TStat : notnull, IEmpiricalStatistics

Parameters

stats TStat

percentile double

The percentile, in [0.9, 1).

Returns

double

The value-at-risk.

Type Parameters

TStat

Exceptions

ArgumentOutOfRangeException

percentile is outside [0.9, 1).