# sla: Single-Loss Approximation for Operational Value at Risk In OpVaR: Statistical Methods for Modeling 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

 `1` ``` 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.

Zou, Christina Z. et al. (2018): "A Monotone Spline Interpolated Closed-Form Approximation for Operational Value-at-Risk." Working Paper (In Preparation)

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ``` ## Not run: #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) ## End(Not run) ```

OpVaR documentation built on May 29, 2018, 9:04 a.m.