Quantile Distance Estimation for Operational Risk: A Practical Application

Journal of Operational Risk Volume 8/Number 2, Summer 2013 (73–102)

30 Pages Posted: 23 May 2014

See all articles by Vincent Lehérissé

Vincent Lehérissé

Bank of the West – BNP Paribas Group

Alexis Renaudin

Aon UK Ltd

Date Written: February 1, 2013

Abstract

Within the loss distribution approach framework, the required capital is the 99.9% value-at-risk of the annual loss distribution, which is based on the fit of the severity and frequency distributions using internal data. The severity estimation is the most difficult to undertake because of the specificity of operational risk data, which sometimes makes common techniques, such as maximum likelihood and the generalized method of moments, unreliable. This paper adapts an alternative method called quantile distance estimation – which is based on the minimization of a distance between empirical and theoretical quantiles – to operational risk modeling in the loss distribution approach framework. We calibrate the different parameters that enable this approach to be used for operational risk and then perform a study comparing it with the common estimation methods that use real data sets from the industry. We show that quantile distance estimation compares favorably with the other methods in an operational risk context.

Keywords: Operational risk; Loss Distribution Approach; Quantile Distance; Maximum Likelihood Estimation; Generalized Method of Moments; Lognormal distribution; Goodness-of-fit tests.

Suggested Citation

Lehérissé, Vincent and Renaudin, Alexis, Quantile Distance Estimation for Operational Risk: A Practical Application (February 1, 2013). Journal of Operational Risk Volume 8/Number 2, Summer 2013 (73–102), Available at SSRN: https://ssrn.com/abstract=2439767

Vincent Lehérissé (Contact Author)

Bank of the West – BNP Paribas Group ( email )

San Francisco, CA 94108
United States

Alexis Renaudin

Aon UK Ltd ( email )

London
United Kingdom

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