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Bayesian vine copulas for modelling dependence in data breach losses

Published online by Cambridge University Press:  03 February 2022

Jia Liu Open the ORCID record for Jia Liu [Opens in a new window] ,
Jackie Li  and
Kevin Daly
Jia Liu
Affiliation:
Research School of Finance, Actuarial Studies & Statistics, College of Business and Economics, Australian National University, Canberra, Australian Capital Territory, Australia
Jackie Li
Affiliation:
Department of Econometrics and Business Statistics, Monash Business School, Monash University, Melbourne, Victoria, Australia
Kevin Daly
Affiliation:
Department of Economics, Finance and Property, School of Business, Western Sydney University, Sydney, New South Wales, Australia
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Abstract

Potentialdata breach losses represent a significant part of operational risk and can be a serious concern for risk managers and insurers. In this paper, we employ the vine copulas under a Bayesian framework to co-model incidences from different data breach types. A full Bayesian approach can allow one to select both the copulas and margins and estimate their parameters in a coherent fashion. In particular, it can incorporate process, parameter, and model uncertainties, and this is very important for applications in risk management under current regulations. We also conduct a series of sensitivity tests on the Bayesian modelling results. Using two public data sets of data breach losses, we find that the overall dependency structure and tail dependence vary significantly between different types of data breaches. The optimally selected vine structure and pairwise copulas suggest more conservative value-at-risk estimates when compared to the other suboptimal copula models.

Keywords

Bayesian vine copulaTail dependenceData breach losses
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 2 , July 2022 , pp. 401 - 424
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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