- QuantLib
- GenericGaussianStatistics
 
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 | |
| 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) | |
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.
| Real gaussianDownsideVariance | ( | ) | const | 
returns the downside variance, defined as
![\[ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} \]](form_248.png) 
, where  = 0 if x > 0 and
 = 0 if x > 0 and  =1 if x <0
 =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
![\[ \frac{\sum w_i (min(0, x_i-target))^2 }{\sum w_i}. \]](form_250.png) 
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
![\[ y = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} \exp (-u^2/2) du \]](form_251.png) 
| 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
Assuming a gaussian distribution it returns the expected loss in case that the loss exceeded a VaR threshold,
![\[ \mathrm{E}\left[ x \;|\; x < \mathrm{VaR}(p) \right], \]](form_252.png) 
that is the average of observations below the given percentile  . Also know as conditional value-at-risk.
. Also know as conditional value-at-risk.
See Artzner, Delbaen, Eber and Heath, "Coherent measures of risk", Mathematical Finance 9 (1999)