Journal of Operational Risk

Risk.net

Various approximations of the total aggregate loss quantile function with application to operational risk

Ross Griffiths and Walid Mnif

  • We explain the mechanics of the empirical aggregate loss bootstrap distribution and develop an analytic approximation to its quantile function.
  • We present various other approximations of the empirical bootstrap quantile function based on techniques in the literature. 
  • We study the impact of empirical moments and large losses in the context of the empirical bootstrap measure of operational risk capital. 
     

A compound Poisson distribution is the sum of independent and identically distributed random variables over a count variable that follows a Poisson distribution. Generally, this distribution is not tractable. However, it has many practical applications that require the estimation of the quantile function at a high percentile, eg, the 99.9th percentile. Without loss of generality, this paper focuses on the application to operational risk. We assume that the support of random variables is nonnegative, discrete and finite. We investigate the mechanics of the empirical aggregate loss bootstrap distribution and suggest different approximations of its quantile function. Furthermore, we study the impact of empirical moments and large losses on the empirical bootstrap capital at the 99.9% confidence level.

To continue reading...

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an indvidual account here: