Statistics tool for gaussian-assumption risk measures. More...
#include <gaussianstatistics.hpp>
Inheritance diagram for GenericGaussianStatistics< Stat >:
Collaboration diagram for GenericGaussianStatistics< Stat >:
Public Types | |
| typedef Stat::value_type | value_type |
Public Member Functions | |
| GenericGaussianStatistics ()=default | |
| 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) More... | |
| Real | gaussianAverageShortfall (Real target) const |
| gaussian-assumption Average Shortfall (averaged shortfallness) More... | |
Detailed Description
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.
Definition at line 40 of file gaussianstatistics.hpp.
Member Typedef Documentation
◆ value_type
| typedef Stat::value_type value_type |
Definition at line 42 of file gaussianstatistics.hpp.
Constructor & Destructor Documentation
◆ GenericGaussianStatistics() [1/2]
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default |
◆ GenericGaussianStatistics() [2/2]
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explicit |
Definition at line 44 of file gaussianstatistics.hpp.
Member Function Documentation
◆ gaussianDownsideVariance()
| 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
Definition at line 53 of file gaussianstatistics.hpp.
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◆ gaussianDownsideDeviation()
| Real gaussianDownsideDeviation | ( | ) | const |
returns the downside deviation, defined as the square root of the downside variance.
Definition at line 60 of file gaussianstatistics.hpp.
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◆ gaussianRegret()
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)
Definition at line 132 of file gaussianstatistics.hpp.
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◆ gaussianPercentile()
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
Definition at line 148 of file gaussianstatistics.hpp.
◆ gaussianTopPercentile()
- Precondition
- percentile must be in range (0%-100%) extremes excluded
Definition at line 163 of file gaussianstatistics.hpp.
◆ gaussianPotentialUpside()
gaussian-assumption Potential-Upside at a given percentile
- Precondition
- percentile must be in range [90%-100%)
Definition at line 171 of file gaussianstatistics.hpp.
◆ gaussianValueAtRisk()
gaussian-assumption Value-At-Risk at a given percentile
- Precondition
- percentile must be in range [90%-100%)
Definition at line 185 of file gaussianstatistics.hpp.
◆ gaussianExpectedShortfall()
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%)
Definition at line 201 of file gaussianstatistics.hpp.
◆ gaussianShortfall()
gaussian-assumption Shortfall (observations below target)
Definition at line 220 of file gaussianstatistics.hpp.
◆ gaussianAverageShortfall()
gaussian-assumption Average Shortfall (averaged shortfallness)
Definition at line 229 of file gaussianstatistics.hpp.