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Modelling Extremal Dependence for Operational Risk by a Bipartite Graph

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  • Oliver Kley
  • Claudia Kluppelberg
  • Sandra Paterlini

Abstract

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails of losses and the heterogeneous dependence structures between them. We then derive estimators for individual as well as aggregated tail risk, measured in terms of Value-at-Risk and Conditional-Tail-Expectation for very high confidence levels, and provide also an asymptotically full capital allocation method. Estimation methods for such tail risk measures and capital allocations are also proposed and tested on simulated data. Finally, by having access to real-world operational risk losses from the Italian banking system, we show that even with a small number of observations, the proposed estimation methods produce reliable estimates, and that quantifying dependence by means of the empirical network has a big impact on estimates at both individual and aggregate level, as well as for capital allocations.

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  • Oliver Kley & Claudia Kluppelberg & Sandra Paterlini, 2019. "Modelling Extremal Dependence for Operational Risk by a Bipartite Graph," Papers 1902.03041, arXiv.org.
    • Handle: RePEc:arx:papers:1902.03041
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    References listed on IDEAS

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    1. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.
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    Cited by:

    1. Tang, Qihe & Tong, Zhiwei & Xun, Li, 2022. "Insurance risk analysis of financial networks vulnerable to a shock," European Journal of Operational Research, Elsevier, vol. 301(2), pages 756-771.
    2. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.

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