- QuantLib
- GenericRiskStatistics
 
empirical-distribution risk measures More...
#include <ql/math/statistics/riskstatistics.hpp>
Inherits S.
| Public Types | |
| typedef S::value_type | value_type | 
| Public Member Functions | |
| Real | semiVariance () const | 
| Real | semiDeviation () const | 
| Real | downsideVariance () const | 
| Real | downsideDeviation () const | 
| Real | regret (Real target) const | 
| Real | potentialUpside (Real percentile) const | 
| potential upside (the reciprocal of VAR) at a given percentile | |
| Real | valueAtRisk (Real percentile) const | 
| value-at-risk at a given percentile | |
| Real | expectedShortfall (Real percentile) const | 
| expected shortfall at a given percentile | |
| Real | shortfall (Real target) const | 
| Real | averageShortfall (Real target) const | 
empirical-distribution risk measures
This class wraps a somewhat generic statistic tool and adds a number of risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on the data distribution as reported by the underlying statistic tool.
| Real semiVariance | ( | ) | const | 
returns the variance of observations below the mean,
![\[ \frac{N}{N-1} \mathrm{E}\left[ (x-\langle x \rangle)^2 \;|\; x < \langle x \rangle \right]. \]](form_265.png) 
See Markowitz (1959).
| Real semiDeviation | ( | ) | const | 
returns the semi deviation, defined as the square root of the semi variance.
| Real downsideVariance | ( | ) | const | 
returns the variance of observations below 0.0,
![\[ \frac{N}{N-1} \mathrm{E}\left[ x^2 \;|\; x < 0\right]. \]](form_266.png) 
| Real downsideDeviation | ( | ) | const | 
returns the downside deviation, defined as the square root of the downside variance.
returns the variance of observations below target,
![\[ \frac{N}{N-1} \mathrm{E}\left[ (x-t)^2 \;|\; x < t \right]. \]](form_267.png) 
See Dembo and Freeman, "The Rules Of Risk", Wiley (2001).
| Real potentialUpside | ( | Real | centile | ) | const | 
potential upside (the reciprocal of VAR) at a given percentile
| Real valueAtRisk | ( | Real | centile | ) | const | 
value-at-risk at a given percentile
| Real expectedShortfall | ( | Real | centile | ) | const | 
expected shortfall at a given percentile
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)
| Real averageShortfall | ( | Real | target | ) | const | 
averaged shortfallness, defined as
![\[ \mathrm{E}\left[ t-x \;|\; x<t \right] \]](form_270.png)