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Robust Estimation of Operational Risk

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  • Nataliya Horbenko
  • Peter Ruckdeschel
  • Taehan Bae

Abstract

According to the Loss Distribution Approach, the operational risk of a bank is determined as 99.9% quantile of the respective loss distribution, covering unexpected severe events. The 99.9% quantile can be considered a tail event. As supported by the Pickands-Balkema-de Haan Theorem, tail events exceeding some high threshold are usually modeled by a Generalized Pareto Distribution (GPD). Estimation of GPD tail quantiles is not a trivial task, in particular if one takes into account the heavy tails of this distribution, the possibility of singular outliers, and, moreover, the fact that data is usually pooled among several sources. Moreover, if, as is frequently the case, operational losses are pooled anonymously, relevance of the fitting data for the respective bank is not self-evident. In such situations, robust methods may provide stable estimates when classical methods already fail. In this paper, optimally-robust procedures MBRE, OMSE, RMXE are introduced to the application domain of operational risk. We apply these procedures to parameter estimation of a GPD at data from Algorithmics Inc. To better understand these results, we provide supportive diagnostic plots adjusted for this context: influence plots, outlyingness plots, and QQ plots with robust confidence bands.

Suggested Citation

  • Nataliya Horbenko & Peter Ruckdeschel & Taehan Bae, 2010. "Robust Estimation of Operational Risk," Papers 1012.0249, arXiv.org, revised Mar 2011.
  • Handle: RePEc:arx:papers:1012.0249
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    References listed on IDEAS

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    1. de Fontnouvelle, Patrick & Dejesus-Rueff, Virginia & Jordan, John S. & Rosengren, Eric S., 2006. "Capital and Risk: New Evidence on Implications of Large Operational Losses," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(7), pages 1819-1846, October.
    2. Mark Carey & René M. Stulz, 2007. "The Risks of Financial Institutions," NBER Books, National Bureau of Economic Research, Inc, number care06-1.
    3. Chavez-Demoulin, V. & Embrechts, P. & Neslehova, J., 2006. "Quantitative models for operational risk: Extremes, dependence and aggregation," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2635-2658, October.
    4. Carey, Mark & Stulz, René M. (ed.), 2007. "The Risks of Financial Institutions," National Bureau of Economic Research Books, University of Chicago Press, number 9780226092850, August.
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    Cited by:

    1. Daoping Yu & Vytaras Brazauskas, 2017. "Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case," Risks, MDPI, vol. 5(3), pages 1-17, September.
    2. Mora Valencia Andrés, 2014. "El uso de la distribución g-h en riesgo operativo," Contaduría y Administración, Accounting and Management, vol. 59(1), pages 123-148, enero-mar.
    3. Heng Z. Chen & Stephen R. Cosslett, 2021. "Semi-nonparametric Estimation of Operational Risk Capital with Extreme Loss Events," Papers 2111.11459, arXiv.org, revised Jul 2022.
    4. Lu Wei & Jianping Li & Xiaoqian Zhu, 2018. "Operational Loss Data Collection: A Literature Review," Annals of Data Science, Springer, vol. 5(3), pages 313-337, September.

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