Classification and Diversification Benefit for Operational Risk Data

15 Pages Posted: 15 Nov 2013 Last revised: 21 Nov 2023

See all articles by Roberto Torresetti

Roberto Torresetti

Università degli Studi di Milano; Intesa SanPaolo

Giacomo Le Pera

illimity Bank

Date Written: January 28, 2014

Abstract

One of the very first step in modeling Operational Risk is designing a classification scheme for operational losses. The aim is to identify risk classes internally as much homogeneous as possible. In doing so one needs to balance the need of a coarse classification scheme so that enough observations are available to estimate consistently the tails of the loss distribution. On the other hand one might want to be able to classify losses in a detailed way so that homogeneity within the class is guaranteed and also to be able to obtain a diversification benefit when estimating the tail of the aggregate loss across classes. Here we will see the conditions that make the classification scheme not relevant. In other words we will see the conditions that make the diversified and undiversified VaR the same. The asymptotic convergence of the diversified and undiversified VaR has already been proven referencing a set of conditions that do not seem the widespread market practice according to the observed range of practices of AMA banks as published by the Basel Committee. Here we prove the same results referencing a set of conditions in line with the observed range of practices. We will also see how despite the theoretical irrelevance of the classification scheme in practice the diversification benefit might still arise due to a slow convergence of the theoretical asymptotic result.

Keywords: Operational Risk, Classification, Loss Distribution Approach, Advanced Measurement Approach, VaR, Diversification, Correlation, Single Loss Approximation, Extreme Events, Sub-exponential Distribution, Regularly Varying Distributions, Poisson Process, Compound Process, Mixture Distribution

JEL Classification: G14, G18, G21, G22, G28, G32

Suggested Citation

Torresetti, Roberto and Le Pera, Giacomo, Classification and Diversification Benefit for Operational Risk Data (January 28, 2014). Available at SSRN: https://ssrn.com/abstract=2354308 or http://dx.doi.org/10.2139/ssrn.2354308

Roberto Torresetti (Contact Author)

Università degli Studi di Milano ( email )

via Festa del Perdono, 7
Milano
Italy

Intesa SanPaolo ( email )

Milan
Italy

Giacomo Le Pera

illimity Bank ( email )

Via Soperga
Milano
Italy

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