Treatment of the Data Collection Threshold in Operational Risk: A Case Study with the Lognormal Distribution

The Journal of Operational Risk, Vol. 7, No. 1, Spring 2012.

33 Pages Posted: 31 Aug 2010 Last revised: 10 Feb 2012

Alexander Cavallo

Northern Trust Corporation

Benjamin Rosenthal

Northern Trust Corporation

Xiao Wang

University of Connecticut - Department of Statistics

Jun Yan

University of Connecticut - Department of Statistics

Date Written: February 1, 2012

Abstract

Among operational risk practitioners there is some confusion about the implications of the loss data collection threshold and the estimation of "truncated" or "shifted" distributions. Claims that "shifted" models result in biased parameter estimates rely on the premise that the "true" model is known to be "truncated" and do not objectively evaluate "shifted" distributions. We systematically analyze the performance of "shifted" and "truncated" lognormal models and illustrate the use of Vuong's LR test for model selection. We conclude that truncated and shifted lognormal models are equally valid or invalid approaches for estimating loss severity with a data collection threshold.

Keywords: Operational risk, Regulatory capital, Loss distribution, Data truncation, Shifted distribution, Vuong's test, Severity distribution, Basel II

JEL Classification: C13, G20, G21, G32

Suggested Citation

Cavallo, Alexander and Rosenthal, Benjamin and Wang, Xiao and Yan, Jun, Treatment of the Data Collection Threshold in Operational Risk: A Case Study with the Lognormal Distribution (February 1, 2012). The Journal of Operational Risk, Vol. 7, No. 1, Spring 2012.. Available at SSRN: https://ssrn.com/abstract=1668939 or http://dx.doi.org/10.2139/ssrn.1668939

Alexander Cavallo (Contact Author)

Northern Trust Corporation ( email )

50 South LaSalle Street
Chicago, IL 60603
United States

Benjamin L. Rosenthal

Northern Trust Corporation ( email )

50 South LaSalle Street
Chicago, IL 60603
United States

Xiao Wang

University of Connecticut - Department of Statistics ( email )

Room 323, Philip E. Austin Building
215 Glenbrook Rd. U-4120
Storrs, CT 06269-4120
United States

Jun Yan

University of Connecticut - Department of Statistics ( email )

Room 323, Philip E. Austin Building
215 Glenbrook Rd. U-4120
Storrs, CT 06269-4120
United States

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