empirical-distribution risk measures More...
#include <ql/math/statistics/riskstatistics.hpp>
Inheritance diagram for GenericRiskStatistics< S >:
Collaboration diagram for GenericRiskStatistics< 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 More... | |
| Real | valueAtRisk (Real percentile) const |
| value-at-risk at a given percentile More... | |
| Real | expectedShortfall (Real percentile) const |
| expected shortfall at a given percentile More... | |
| Real | shortfall (Real target) const |
| Real | averageShortfall (Real target) const |
Detailed Description
class QuantLib::GenericRiskStatistics< S >
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.
- Examples
- DiscreteHedging.cpp, and MarketModels.cpp.
Definition at line 41 of file riskstatistics.hpp.
Member Typedef Documentation
◆ value_type
| typedef S::value_type value_type |
Definition at line 43 of file riskstatistics.hpp.
Member Function Documentation
◆ semiVariance()
| Real semiVariance |
returns the variance of observations below the mean,
\[ \frac{N}{N-1} \mathrm{E}\left[ (x-\langle x \rangle)^2 \;|\; x < \langle x \rangle \right]. \]
See Markowitz (1959).
Definition at line 130 of file riskstatistics.hpp.
◆ semiDeviation()
| Real semiDeviation |
returns the semi deviation, defined as the square root of the semi variance.
Definition at line 135 of file riskstatistics.hpp.
◆ downsideVariance()
| Real downsideVariance |
returns the variance of observations below 0.0,
\[ \frac{N}{N-1} \mathrm{E}\left[ x^2 \;|\; x < 0\right]. \]
Definition at line 140 of file riskstatistics.hpp.
◆ downsideDeviation()
| Real downsideDeviation |
returns the downside deviation, defined as the square root of the downside variance.
Definition at line 145 of file riskstatistics.hpp.
◆ regret()
returns the variance of observations below target,
\[ \frac{N}{N-1} \mathrm{E}\left[ (x-t)^2 \;|\; x < t \right]. \]
See Dembo and Freeman, "The Rules Of Risk", Wiley (2001).
Definition at line 152 of file riskstatistics.hpp.
◆ potentialUpside()
potential upside (the reciprocal of VAR) at a given percentile
- Precondition
- percentile must be in range [90%-100%)
Definition at line 169 of file riskstatistics.hpp.
◆ valueAtRisk()
value-at-risk at a given percentile
- Precondition
- percentile must be in range [90%-100%)
Definition at line 180 of file riskstatistics.hpp.
◆ expectedShortfall()
expected shortfall at a given percentile
returns the expected loss in case that the loss exceeded a VaR threshold,
\[ \mathrm{E}\left[ x \;|\; x < \mathrm{VaR}(p) \right], \]
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 191 of file riskstatistics.hpp.
◆ shortfall()
probability of missing the given target, defined as
\[ \mathrm{E}\left[ \Theta \;|\; (-\infty,\infty) \right] \]
where
\[ \Theta(x) = \left\{ \begin{array}{ll} 1 & x < t \\ 0 & x \geq t \end{array} \right. \]
Definition at line 208 of file riskstatistics.hpp.
◆ averageShortfall()
averaged shortfallness, defined as
\[ \mathrm{E}\left[ t-x \;|\; x<t \right] \]
Definition at line 214 of file riskstatistics.hpp.