Formula: ES_p = (VaR_p + sigma - xi u) / (1 - xi)
Usage
Evespot(u, sigma, xi, VaR)
Arguments
- u
Threshold the GPD was fitted above.
- sigma
GPD scale, strictly positive.
- xi
GPD shape.
- VaR
Value-at-risk at the level of interest.
Value
List with ES, estimate, ratio,
xi, method.
Details
E[X | X > VaR] for the generalised Pareto tail. The mean excess of a
GPD is finite only for xi < 1, so xi >= 1 is refused rather than
returned as a number. At xi = 0 the expression collapses to
VaR + sigma, the memoryless exponential mean excess.
References
McNeil & Frey (2000), J. Empirical Finance 7(3-4):271-300.
Examples
Evespot(u = 1, sigma = 0.5, xi = 0.1, VaR = 2)
#> $ES
#> [1] 2.666667
#>
#> $estimate
#> [1] 2.666667
#>
#> $ratio
#> [1] 1.333333
#>
#> $xi
#> [1] 0.1
#>
#> $method
#> [1] "GPD expected shortfall above a POT threshold"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
