Estimation of Truncated Data Samples in Operational Risk Modeling

32 Pages Posted: 27 Dec 2012 Last revised: 23 Apr 2014

See all articles by Bakhodir Ergashev

Bakhodir Ergashev

EY

Konstantin Pavlikov

University of Florida - Department of Industrial and Systems Engineering

Stanislav P. Uryasev

University of Florida

Evangelos Sekeris

Federal Reserve Banks - Federal Reserve Bank of Richmond; Federal Reserve Bank of Boston

Multiple version iconThere are 2 versions of this paper

Date Written: April 22, 2014

Abstract

This paper addresses challenges of estimating operational risk regulatory capital when a loss sample is truncated from below at a data collection threshold. Recent operational risk literature reports that the attempts to estimate loss distributions by the maximum likelihood method are not always successful under the truncation approach that accounts for the existence of censored losses - the likelihood surface is sometimes ascending with no global solution. The literature o ers an alternative called the shifting approach, which estimates the loss distribution without taking into account censored losses. We present a necessary and sucient condition for the existence of the global solution to the likelihood maximization problem under the truncation approach when the true loss distribution is lognormal, and derive a practically explicit expression for the global solution. We show by a simulation study that, as the sample size increases, the capital bias by the truncation approach declines while the bias by the shifting approach does not.

Keywords: Operational risk, VaR, Censored data, Truncation, Method of moments, Maximum likelihood

JEL Classification: G17, G18, G32, C13, C53, C54

Suggested Citation

Ergashev, Bakhodir and Pavlikov, Konstantin and Uryasev, Stanislav P. and Sekeris, Evangelos, Estimation of Truncated Data Samples in Operational Risk Modeling (April 22, 2014). Available at SSRN: https://ssrn.com/abstract=2193493 or http://dx.doi.org/10.2139/ssrn.2193493

Konstantin Pavlikov

University of Florida - Department of Industrial and Systems Engineering ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States

Stanislav P. Uryasev

University of Florida ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-3091 (Phone)
352-392-3537 (Fax)

HOME PAGE: http://www.ise.ufl.edu/uryasev/

Evangelos Sekeris

Federal Reserve Banks - Federal Reserve Bank of Richmond ( email )

P.O. Box 27622
Richmond, VA 23261
United States

Federal Reserve Bank of Boston ( email )

600 Atlantic Avenue
Boston, MA 02210
United States

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