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Risks 2017, 5(3), 49; doi:10.3390/risks5030049

Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case

1
School of Computer Science and Mathematics, University of Central Missouri, Warrensburg, MO 64093, USA
2
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Albert Cohen
Received: 27 April 2017 / Revised: 15 August 2017 / Accepted: 1 September 2017 / Published: 13 September 2017
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Abstract

Over the last decade, researchers, practitioners, and regulators have had intense debates about how to treat the data collection threshold in operational risk modeling. Several approaches have been employed to fit the loss severity distribution: the empirical approach, the “naive” approach, the shifted approach, and the truncated approach. Since each approach is based on a different set of assumptions, different probability models emerge. Thus, model uncertainty arises. The main objective of this paper is to understand the impact of model uncertainty on the value-at-risk (VaR) estimators. To accomplish that, we take the bank’s perspective and study a single risk. Under this simplified scenario, we can solve the problem analytically (when the underlying distribution is exponential) and show that it uncovers similar patterns among VaR estimates to those based on the simulation approach (when data follow a Lomax distribution). We demonstrate that for a fixed probability distribution, the choice of the truncated approach yields the lowest VaR estimates, which may be viewed as beneficial to the bank, whilst the “naive” and shifted approaches lead to higher estimates of VaR. The advantages and disadvantages of each approach and the probability distributions under study are further investigated using a real data set for legal losses in a business unit (Cruz 2002). View Full-Text
Keywords: asymptotics; data truncation; delta method; model validation; operational risk; VaR estimation asymptotics; data truncation; delta method; model validation; operational risk; VaR estimation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Yu, D.; Brazauskas, V. Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case. Risks 2017, 5, 49.

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