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15 - Validation of Risk Aggregation in Economic Capital Models

Published online by Cambridge University Press:  02 March 2023

By
Ibrahim Ergen ,
Hulusi Inanoglu  and
David Lynch
Edited by
David Lynch ,
Iftekhar Hasan  and
Akhtar Siddique
David Lynch
Affiliation:
Federal Reserve Board of Governors
Iftekhar Hasan
Affiliation:
Fordham University Graduate Schools of Business
Akhtar Siddique
Affiliation:
Office of the Comptroller of the Currency
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Summary

This chapter implements a coherent statistical framework for validation of economic capital models via copula methods using a unique dataset to aggregate credit, market, operational, and interest rate risks. This framework includes benchmarking with alternative copula models and backtesting with alternative penalty functions, in addition to stability and stress tests of economic capital estimates. The analysis is expanded to include the latest supervisory guidance on model validation (i.e. SR11-7) and Basel Accord changes (i.e., Basel III). Second, proprietary confidential loss data is used from major US banks for market risk and operational risk. Lastly, both analytic and visual goodness-of-fit tests for copula models are included. For the data used in this study, the T copula with 4 degree of freedom provides a good statistical fit, superior backtesting performance, reasonable model stability and sufficient sensitivity to stress. In addition, the results provide some support for regulators’ hesitation to recognize diversification benefits by demonstrating a wide range of diversification benefits across risk types under different dependence models.

Keywords

Economic capital
Type
Chapter
Information
Validation of Risk Management Models for Financial Institutions
Theory and Practice
 , pp. 379 - 421
Publisher: Cambridge University Press
Print publication year: 2023

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References

Abdymomunov, A. and Ergen, I. (2017). Tail dependence and systemic risk in operational losses of US Banking Industry. International Review of Finance, 17(2), 177–204.Google Scholar
Alessandri, Piergiorgio and Drehmann, Mathias. (2010). An economic capital model integrating credit and interest rate risk in the banking book. Journal of Banking and Finance, 34, 730–742.Google Scholar
Basel Committee on Banking Supervision. (2009). Range of practices and issues in economic capital frameworks. Bank for International Settlements, Basel, March.Google Scholar
Basel Committee on Banking Supervision. (2010). Developments in modelling risk aggregation. Bank for International Settlements, Basel, October.Google Scholar
Basel Committee on Banking Supervision. (2013). Principles for effective risk data aggregation and risk reporting. Bank for International Settlements, Basel, January.Google Scholar
Breymann, W., Dias, A., Embrechts, , P. (2003). Dependence structures for multivariate high-frequency data in finance. Quantitative Finance, 3(1), 1–14.CrossRefGoogle Scholar
Dobric, Jadran and Schmid, Friedrich. (2007). A goodness of fit test for copulas based on Rosenblatt’s transformation. Computational Statistics & Data Analysis, 51(9), 4633–4642.Google Scholar
Drehmann, Mathias, Sorensen, Steffen and Stringa, Marco. (2010). The integrated impact of credit and interest rate risk on banks: A dynamic framework and stress testing application, Journal of Banking and Finance, 34, 713–729.Google Scholar
Ergen, Ibrahim. (2015). Two-step methods in VaR prediction and the importance of fat tails. Quantitative Finance, 15(6), 1013–1030.Google Scholar
Federal Reserve. (2011). Supervisory guidance on model risk management, SR Letter 11–7.Google Scholar
Giacomini, Raffaella and Komunjer, Ivana. (2005). Evaluation and combination of conditional quantile forecasts. Journal of Business & Economic Statistics, 23(4), 416–431.Google Scholar
Genest, Christian, Remillard, Bruno, and Beaudoin, David. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44(2), 199–213.Google Scholar
Genest, Christian and Remillard, Bruno. (2004). Test of independence and randomness based on the empirical copula process. Test, 13(2), 335–369.Google Scholar
Hofert, Marius, Machler, Martin, and McNeil, , Alexander J. (2012). Likelihood inference for Archimedean copulas in high dimensions under known margins. Journal of Multivariate Analysis, 110, 133–150.Google Scholar
Hofert, Marius and Machler, Martin. (2013). A Graphical goodness-of-fit test for dependence models in higher dimensions. Journal of Computational and Graphical Statistics, 23(3), 700–716.CrossRefGoogle Scholar
Inanoglu, Hulusi and Jacobs, Michael. (2009). Models for risk aggregation and sensitivity analysis: An application to bank economic capital. Journal of Risk and Financial Management, 2(1), 118–189.Google Scholar
Jorion, P. (2006). Value at Risk: The Benchmark for Managing Financial Risk, Third Edition, New York, N.Y.: McGraw Hill.Google Scholar
Koenker, Roger, and Bassett, Gilbert. (1978). Regression quantiles. Econometrica, 46(1), 33–50.Google Scholar
Kuester, Keither, Mittnik, Stefan, and Paolella, Mark S. (2006). Value-at-Risk prediction: A comparison of alternative strategies. Journal of Financial Econometrics, 4(Winter), 53–89.Google Scholar
Li, Jianping, Zhu, Xiaoqian, Lee, Cheng-Few, Wu, Dengsheng, Feng, Jichuang, and Shi, Yong. (2015). On the aggregation of credit, market and operational risks. Review of Quantitative Finance and Accounting, 44, 161–189.Google Scholar
Liang, Changzhi, Zhu, Xiaoqian, Li, Yilin, Sun, Xiaolei, Chen, Jianming and Li, Jianping. (2013). Integrating credit and market risk: A factor copula based method. Procedia Computer Science, 17, 657–663.Google Scholar
McNeil, Alexander J., Embrechts, Paul, and Frey, Rudiger. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton: Princeton University Press.Google Scholar
Mester, L.J. (1996). A study of bank efficiency taking into account risk-preferences. Journal of Banking and Finance, 20(6), 1025–1045.Google Scholar
Nelson, Roger B. (2006). An Introduction to Copulas. New York: Springer-Verlag.Google Scholar
Rosenberg, J., and Schuermann, T. (2006). A General approach to integrated risk management with skewed, fat-tailed risks. Journal of Financial Economics, 79, 569–614.Google Scholar
Rosenblatt, Murray. (1952). Remarks on a multivariate transformation. The Annals of Mathematical Statistics, 23(3), 470–72.Google Scholar
Sklar, Abe. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris, 8, 229–231.Google Scholar
Trivedi, Pravin K. and Zimmer, David M. (2007). Copula modeling: An introduction for practitioners. Foundations and Trends in Econometrics, 1(1), 1–111.Google Scholar
Yi, Shanli , Li, Jianping, Zhu, Xiaoqian and Feng, Jichuang. (2012). Mutual information based copulas to aggregate banking risks. Proceedings of the Fifth International Conference on Business Intelligence and Financial Engineering.Google Scholar

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