GaussianStatistics Class Template Reference

#include <ql/Math/gaussianstatistics.hpp>

List of all members.


Detailed Description

template<class Stat>
class QuantLib::GaussianStatistics< Stat >

Statistics tool for gaussian-assumption risk measures.

It can calculate gaussian assumption risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on the mean and variance provided by the template class


Public Member Functions

 GaussianStatistics (const Stat &s)
Gaussian risk measures
Real gaussianDownsideVariance () const
Real gaussianDownsideDeviation () const
Real gaussianRegret (Real target) const
Real gaussianPercentile (Real percentile) const
Real gaussianPotentialUpside (Real percentile) const
 gaussian-assumption Potential-Upside at a given percentile

Real gaussianValueAtRisk (Real percentile) const
 gaussian-assumption Value-At-Risk at a given percentile

Real gaussianExpectedShortfall (Real percentile) const
 gaussian-assumption Expected Shortfall at a given percentile

Real gaussianShortfall (Real target) const
 gaussian-assumption Shortfall (observations below target)

Real gaussianAverageShortfall (Real target) const
 gaussian-assumption Average Shortfall (averaged shortfallness)


Member Function Documentation

Real gaussianDownsideVariance  )  const
 

returns the downside variance, defined as

\[ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} \]

, where $ \theta $ = 0 if x > 0 and $ \theta $ =1 if x <0

Real gaussianDownsideDeviation  )  const
 

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

Real gaussianRegret Real  target  )  const
 

returns the variance of observations below target

\[ \frac{\sum w_i (min(0, x_i-target))^2 }{\sum w_i}. \]

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

Real gaussianPercentile Real  percentile  )  const
 

gaussian-assumption y-th percentile, defined as the value x such that

\[ y = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} \exp (-u^2/2) du \]

Real gaussianPotentialUpside Real  percentile  )  const
 

gaussian-assumption Potential-Upside at a given percentile

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

Real gaussianValueAtRisk Real  percentile  )  const
 

gaussian-assumption Value-At-Risk at a given percentile

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

Real gaussianExpectedShortfall Real  percentile  )  const
 

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,

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

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)


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