Encyclopedia of Financial Models III

Modeling Operational Loss Distributions

ANNA CHERNOBAI, PhD

Assistant Professor of Finance, M. J. Whitman School of Management, Syracuse University

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: A major risk faced by financial entities is operational risk. In general terms, operational risk is the risk of loss resulting from inadequate or failed internal processes, people, or systems or from external events. The two principal approaches in modeling operational loss distributions are the nonparametric approach and the parametric approach. It is important to employ a model that captures tail events and for this reason in operational risk modeling, distributions that are characterized as light-tailed distributions should be used with caution.

For financial entities, representing a stream of uncertain operational losses with a specified model is a difficult task: Data can be wrongly recorded, fuzzy, incomplete (e.g., truncated or censored), or simply limited. Two main approaches may be undertaken: nonparametric and parametric. In this entry, we focus on the nonparametric approach, common loss distributions, and mixture distributions. We begin by reviewing the nonparametric approach to modeling operational losses and then proceed to the parametric approach and review ...