Modeling Multivariate Operational Losses Via Copula-Based Distributions with G-and-H Marginals

32 Pages Posted: 23 Feb 2022

See all articles by Marco Bee

Marco Bee

University of Trento - Department of Economics and Management

Julien Hambuckers

University of Liège - HEC Liège

Date Written: July 14, 2021

Abstract

We propose a family of copula-based multivariate distributions with g-and-h marginals. After studying the properties of the distribution, we develop a two-step estimation strategy and analyze via simulation the sampling distribution of the estimators. The methodology is used for the analysis of a seven-dimensional data set containing 40 871 operational losses. The empirical evidence suggests that a distribution based on a single copula is not flexible enough, and thus we model the dependence structure by means of vine copulas. We show that the approach based on regular vines improves the fit. Moreover, even though losses corresponding to different event types are found to be dependent, the assumption of perfect positive dependence is not supported by our analysis. As a result, the value-at-risk of the total operational loss distribution obtained from the copula-based technique is substantially smaller at high confidence levels with respect to the one obtained using the common practice of summing the univariate value-at-risks.

Keywords: loss model, dependence structure, vine copula, value-at-risk, regulatory capital

Suggested Citation

Bee, Marco and Hambuckers, Julien, Modeling Multivariate Operational Losses Via Copula-Based Distributions with G-and-H Marginals (July 14, 2021). Journal of Operational Risk, Vol. 17, No. 1, 2021, Available at SSRN: https://ssrn.com/abstract=4039880

Marco Bee (Contact Author)

University of Trento - Department of Economics and Management ( email )

Via Inama 5
I-38122 Trento
Italy
+39-0461-282296 (Phone)
+39-0461-282222 (Fax)

Julien Hambuckers

University of Liège - HEC Liège ( email )

rue Louvrex 14
Liège, 4000
Belgium

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