sla: Single-Loss Approximation for Operational Value at Risk

In OpVaR: Statistical Methods for Modelling Operational Risk

Description

Given the object opriskmodel using the single-loss approximation a list of alpha-quantiles is created for every cell in opriskmodel.

Usage

  sla(opriskmodel, alpha, xi_low = 0.8, xi_high = 1.2, plot = FALSE)

Arguments

opriskmodel	Object containing the parameters for the severities and the frequencies
alpha	Level of the quantile for the total loss-process of the single-loss-approximation
xi_low	Lower interpolation-point for the spline-function, standard value = 0.8
xi_high	Upper interpolation-point for the spline-function, standard value = 1.2
plot	Plot of the interpolated correction term if xi is between xi_low and xi_high, standard value = FALSE

Details

In the first step the tailindex of the severity distribution is determined. If it does not lie in the critical zone, i.e., not between xi_low and xi_high, the closed-form single-loss approximation from Degen is used. If the tailindex lies in the critical zone, then the R-function splinefun with method "hyman" is used to create a spline with given data points xi lying in [xi_low - 0.2, xi_low] and [xi_high, xi_high + 0.2] using the value at xi = 1 as an anchor. A plot of the interpolation is provided such that user-defined adjustment of xi_low and xi_high is possible.

Author(s)

Benedikt Graswald, Jixuan Wang, Christina Zou

References

Bocker, Klaus, and Claudia Kluppelberg. "Operational VaR: a closed-form approximation." Risk-London-Rsik Magazine Limited- 18.12 (2005): 90.

Degen, Matthias. "The calculation of minimum regulatory capital using single-loss approximations." The Journal of Operational Risk 5.4 (2010): 3.

Examples

  
  #Example: SLA for the spliced log-gamma gpd model (tail-index = 0.014, no interpolation required)
  opriskmodel = list()
  opriskmodel[[1]] = list()
  opriskmodel[[1]]$sevdist = buildSplicedSevdist("lgamma", c(1.23, 0.012), 
                                                 "gpd", c(200, 716, 0.014), 2000, 0.8)
  opriskmodel[[1]]$freqdist = buildFreqdist("pois", 50)
  
  #Example: SLA for the spliced log-gamma gpd model (tail-index = 0.9, interpolation performed)
  opriskmodel[[2]] = list()
  opriskmodel[[2]]$sevdist = buildSplicedSevdist("lgamma", c(1.23, 0.012), 
                                                 "gpd", c(200, 716, 0.9), 2000, 0.8)
  opriskmodel[[2]]$freqdist = buildFreqdist("pois", 50)
  
  sla(opriskmodel, alpha = 0.95) 
  
  #generate plot if interpolation was performed
  sla(opriskmodel, alpha = 0.95, plot = TRUE) 
  
  
  

OpVaR documentation built on Sept. 8, 2021, 5:07 p.m.