Journal of Risk Model Validation

A central limit theorem formulation for empirical bootstrap value-at-risk

Peter Mitic and Nicholas Bloxham

  • An alternative to the empirical bootstrap method for estimating minimum operational risk capital is proposed, based on the Central Limit Theorem
  • The proposed method is calibrated on a set of commonly used fat-tailed distributions, appropriate for operational risk capital calculations
  • The proposed method is tested against actual loss distributions, and found to be more conservative than using the empirical bootstrap.  As such it is a more prudent measure.

In this paper, the importance of the empirical bootstrap (EB) in assessing minimal operational risk capital is discussed, and an alternative way of estimating minimal operational risk capital using a central limit theorem (CLT) formulation is presented. The results compare favorably with risk capital obtained by fitting appropriate distributions to the same data. The CLT formulation is significant in validation because it provides an alternative approach to the calculation that is independent of both the empirical severity distribution and any dependent fitted distribution.

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