Addressing Impact of Truncation and Parameter Uncertainty on Operational Risk Estimates
CSIRO Mathematical & Information Sciences
Pavel V. Shevchenko
CSIRO Mathematics, Informatics and Statistics
affiliation not provided to SSRN
The Journal of Operational Risk, Vol. 2, No. 4, pp. 3-26, 2007
Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the Poisson and Lognormal distributions respectively. Two cases of ignoring data truncation are studied: the "naive model" - fitting a Lognormal distribution with support on a positive semi-infinite interval, and "shifted model" - fitting a Lognormal distribution shifted to the truncation level. For all practical cases, the "naive model" leads to underestimation (that can be severe) of the 0.999 quantile. The "shifted model" overestimates the 0.999 quantile except some cases of small underestimation for large truncation levels. Conservative estimation of capital charge is usually acceptable and the use of the "shifted model" can be justified while the "naive model" should not be allowed. However, if parameter uncertainty is taken into account (in practice it is often ignored), the "shifted model" can lead to considerable underestimation of capital charge. This is demonstrated with a practical example.
Keywords: operational risk, truncated data, Poisson-Lognormal compound distribution, loss distribution approach
JEL Classification: C11, C40, G28, G32Accepted Paper Series
Date posted: January 15, 2009
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo6 in 0.390 seconds