GenericGaussianStatistics< Stat > Class Template Reference

Statistics tool for gaussian-assumption risk measures. More...

`#include <ql/math/statistics/gaussianstatistics.hpp>`

Inherits Stat.

## Public Types

typedef Stat::value_type | value_type

## Public Member Functions

| GenericGaussianStatistics (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 More...
Real | gaussianValueAtRisk (Real percentile) const
| gaussian-assumption Value-At-Risk at a given percentile More...
Real | gaussianExpectedShortfall (Real percentile) const
| gaussian-assumption Expected Shortfall at a given percentile More...
Real | gaussianShortfall (Real target) const
| gaussian-assumption Shortfall (observations below target)
Real | gaussianAverageShortfall (Real target) const
| gaussian-assumption Average Shortfall (averaged shortfallness)

## Detailed Description

### template<class Stat>
class QuantLib::GenericGaussianStatistics< Stat >

Statistics tool for gaussian-assumption risk measures.

This class wraps a somewhat generic statistic tool and adds a number of gaussian risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on the mean and variance provided by the underlying statistic tool.

## 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

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

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

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)

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