Understanding Operational Risk Capital Approximations: First and Second Orders
We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA). Our emphasis is to focus on the important loss processes with regard to those that contribute most to capital, the so called high consequence, low frequency loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard); Expected Shortfall (ES) and the Spectral Risk Measure. These then form the capital approximations.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Adrian Blundell-Wignall & Paul Atkinson, 2010. "Thinking beyond Basel III: Necessary Solutions for Capital and Liquidity," OECD Journal: Financial Market Trends, OECD Publishing, vol. 2010(1), pages 9-33.
- Anil K. Kashyap & Jeremy C. Stein, 2004. "Cyclical implications of the Basel II capital standards," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q I, pages 18-31.
- Peters, Gareth W. & Byrnes, Aaron D. & Shevchenko, Pavel V., 2011. "Impact of insurance for operational risk: Is it worthwhile to insure or be insured for severe losses?," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 287-303, March.
- Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
- Peters, Gareth W. & Shevchenko, Pavel V. & Young, Mark & Yip, Wendy, 2011. "Analytic loss distributional approach models for operational risk from the α-stable doubly stochastic compound processes and implications for capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 565-579.
- Decamps, Jean-Paul & Rochet, Jean-Charles & Roger, Benoit, 2004.
"The three pillars of Basel II: optimizing the mix,"
Journal of Financial Intermediation,
Elsevier, vol. 13(2), pages 132-155, April.
- Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
- Li, Jinzhu & Tang, Qihe, 2010. "A note on max-sum equivalence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1720-1723, December.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1303.2910. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.