An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates

42 Pages Posted: 9 Aug 2016

See all articles by Valérie Chavez-Demoulin

Valérie Chavez-Demoulin

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Paul Embrechts

Swiss Federal Institute of Technology Zurich; Swiss Finance Institute

Marius Hofert

ETH Zurich, RiskLab, Department of Mathematics

Date Written: September 2016

Abstract

A general methodology for modeling loss data depending on covariates is developed. The parameters of the frequency and severity distributions of the losses may depend on covariates. The loss frequency over time is modeled with a nonhomogeneous Poisson process with rate function depending on the covariates. This corresponds to a generalized additive model, which can be estimated with spline smoothing via penalized maximum likelihood estimation. The loss severity over time is modeled with a nonstationary generalized Pareto distribution (alternatively, a generalized extreme value distribution) depending on the covariates. Since spline smoothing cannot directly be applied in this case, an efficient algorithm based on orthogonal parameters is suggested. The methodology is applied both to simulated loss data and a database of operational risk losses collected from public media. Estimates, including confidence intervals, for risk measures such as Value‐at‐Risk as required by the Basel II/III framework are computed. Furthermore, an implementation of the statistical methodology in R is provided.

Suggested Citation

Chavez-Demoulin, Valérie and Embrechts, Paul and Hofert, Marius, An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates (September 2016). Journal of Risk and Insurance, Vol. 83, Issue 3, pp. 735-776, 2016, Available at SSRN: https://ssrn.com/abstract=2820366 or http://dx.doi.org/10.1111/jori.12059

Valérie Chavez-Demoulin (Contact Author)

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Anthropole
Lausanne, 1015
Switzerland

HOME PAGE: http://https://www.hec.unil.ch/people/vchavez&vue=contact&set_language=en&cl=en

Paul Embrechts

Swiss Federal Institute of Technology Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Marius Hofert

ETH Zurich, RiskLab, Department of Mathematics ( email )

Rämistrasse 101
Zurich, 8092
Switzerland

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