GaussianStatistics Class Template Reference

#include <gaussianstatistics.hpp>

List of all members.


Detailed Description

template<class Stat>
class QuantLib::Math::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

Gaussian risk measures
double gaussianDownsideVariance () const
double gaussianDownsideDeviation () const
double gaussianRegret (double target) const
double gaussianPercentile (double percentile) const
double gaussianPotentialUpside (double percentile) const
 gaussian-assumption Potential-Upside at a given percentile

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

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

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

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


Member Function Documentation

double 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

double gaussianDownsideDeviation  )  const
 

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

double gaussianRegret double  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)

double gaussianPercentile double  percentile  )  const
 

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

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

double gaussianPotentialUpside double  percentile  )  const
 

gaussian-assumption Potential-Upside at a given percentile

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

double gaussianValueAtRisk double  percentile  )  const
 

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

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

double gaussianExpectedShortfall double  percentile  )  const
 

gaussian-assumption Expected Shortfall at a given percentile

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


The documentation for this class was generated from the following file:

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