Formula: VaR_p = u + (sigma/xi) (((1-p)/zeta_u)^(-xi) - 1)
Usage
Evvarpot(u, sigma, xi, zeta_u, p)
Arguments
- u
Threshold.
- sigma
GPD scale, strictly positive.
- xi
GPD shape.
- zeta_u
Exceedance rate P(X > u), in (0, 1].
- p
VaR level in (0, 1); must exceed 1 - zeta_u.
Value
List with VaR, estimate, tail_prob,
p, method.
Details
Inverting the tail estimate
P(X > x) = zeta_u (1 + xi (x-u)/sigma)^(-1/xi). The xi = 0 limit is
u + sigma log(zeta_u/(1-p)), used when |xi| is below 1e-12 so the
formula stays continuous.
References
McNeil & Frey (2000), J. Empirical Finance 7(3-4):271-300.
Examples
Evvarpot(u = 1, sigma = 0.5, xi = 0.1, zeta_u = 0.1, p = 0.99)
#> $VaR
#> [1] 2.294627
#>
#> $estimate
#> [1] 2.294627
#>
#> $tail_prob
#> [1] 0.01
#>
#> $p
#> [1] 0.99
#>
#> $method
#> [1] "GPD value-at-risk above a POT threshold"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
