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 gaussianTopPercentile (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 gaussianTopPercentile Real  percentile  )  const
 

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

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)