GenericRiskStatistics Class Template Reference

#include <ql/Math/riskstatistics.hpp>

List of all members.


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 tool.

Todo:
add historical annualized volatility


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

Real valueAtRisk (Real percentile) const
 value-at-risk at a given percentile

Real expectedShortfall (Real percentile) const
 expected shortfall at a given percentile

Real shortfall (Real target) const
Real averageShortfall (Real target) const


Member Function Documentation

Real semiVariance  )  const
 

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).

Real semiDeviation  )  const
 

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

Real downsideVariance  )  const
 

returns the variance of observations below 0.0,

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

Real downsideDeviation  )  const
 

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

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).

Real potentialUpside Real  centile  )  const
 

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

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

Real valueAtRisk Real  centile  )  const
 

value-at-risk at a given percentile

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

Real expectedShortfall Real  percentile  )  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)

Real shortfall Real  target  )  const
 

probability of missing the given target, defined as

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

where

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

Real averageShortfall Real  target  )  const
 

averaged shortfallness, defined as

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


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