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Treatment of the Data Collection Threshold in Operational Risk: A Case Study with the Lognormal Distribution (Cavallo A., Rosenthal B., Yan J.)

Basel I-III Risk-taking and Risk Management

Abstract Among operational risk practitioners there is some confusion about the implications of using a "truncated" or "shifted" distribution to model loss severity when there is a data collection threshold. Several studies claim that "shifted" models are biased when there is a data collection threshold. By starting with the premise that "true'' model is known to be "truncated," these papers fail to objectively test the impact of alternate methodologies. In this study, we perform a systematic analysis of the performance of "shifted" and "truncated" models under a variety of conditions and use the Vuong likelihood ratio test to select among competing loss severity distributions. Using the lognormal distribution as a case study, we have several findings of practical importance to the operational risk analysts. Overall, we conclude that shifted models are a potentially useful class of severity model for use in operational risk, and that the truncated lognormal model and the shifted lognormal model are equally valid or invalid approaches for estimating loss severity distributions in the presence of a data collection threshold.
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Libref/ Cavallo A., Rosenthal B., Yan J. (2010) "Treatment of the Data Collection Threshold in Operational Risk: A Case Study with the Lognormal Distribution", pp. 1 - 31
© Программирование — Александр Красильников, 2008
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