QuantLib 0.3.6
User manual
Introduction to QuantLib
QuantLib components
Reference manual
GaussianStatistics Class Template Reference
#include <ql/Math/gaussianstatistics.hpp>
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 | |
| 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
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returns the downside variance, defined as
, where |
![\[ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} \]](form_160.png)
= 0 if x > 0 and
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returns the downside deviation, defined as the square root of the downside variance. |
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returns the variance of observations below target
See Dembo, Freeman "The Rules Of Risk", Wiley (2001) |
![\[ \frac{\sum w_i (min(0, x_i-target))^2 }{\sum w_i}. \]](form_162.png)
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gaussian-assumption y-th percentile, defined as the value x such that
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![\[ y = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} \exp (-u^2/2) du \]](form_163.png)
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gaussian-assumption Potential-Upside at a given percentile
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gaussian-assumption Value-At-Risk at a given percentile
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gaussian-assumption Expected Shortfall at a given percentile
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