Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T21:18:59.242Z Has data issue: false hasContentIssue false
  • English
  • Français

A scaling model for severity of operational losses using generalized additive models for location scale and shape (GAMLSS)

Published online by Cambridge University Press:  30 October 2012

Amandha Ganegoda  and
John Evans
Amandha Ganegoda*
Affiliation:
School of Actuarial Studies, Australian School of Business, Sydney, Australia
John Evans
Affiliation:
School of Actuarial Studies, Australian School of Business, Sydney, Australia
*
*Correspondence to: Amandha Ganegoda, School of Actuarial Studies, Australian School of Business, UNSW, Sydney NSW 2052, Australia. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we investigate the problem of how to combine operational losses collected from various banks of different sizes and loss reporting thresholds in order to estimate the distribution of operational loss severities for a bank of a given size. We model the severity of operational losses by using the extreme value theory to account for the reporting bias of the external data, and a regression analysis based on the GAMLSS framework to model the scaling properties of operational losses. In contrast to previous studies on the scaling problem, our analysis gives particular emphasis to the scaling properties of the tail of the loss distribution. Contrary to existing knowledge, we find that the size of a bank is an important determinant of the severity of operational losses and that the tail index of the distribution is negatively correlated with the size of the bank. The results indicate that for very large banks, distribution of the operational loss severity can be extremely heavy tailed (i.e. tail index less than 1), a finding which have significant implications for capital calculation as well as for risk management. Furthermore, we also demonstrate that the capital estimates provided by our model is consistent with the industry standards and the model can be used by individual banks to simulate data to complement their internal data.

Keywords

Operational riskGeneralized Additive Models for Location Scale And Shape (GAMLSS)Scaling modelsPrudential Regulation of Banks

JEL classification

C30: General C35: Discrete Regression and Qualitative Choice Models • Discrete Regressors • Proportions G21: Banks • Depository Institutions • Micro Finance Institutions • Mortgages C38: Classification Methods • Cluster Analysis • Principal Components • Factor Models G28: Government Policy and Regulation
Type
Papers
Information
Annals of Actuarial Science , Volume 7 , Issue 1: Special issue on Enterprise Risk Management , March 2013 , pp. 61 - 100
Copyright
Copyright © Institute and Faculty of Actuaries 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Altamuro, J., Beatty, A. (2010). How does internal control regulation affect financial reporting? Journal of Accounting and Economics, 49(1-2), 58–74.Google Scholar
Arnold, B.C., Balakrishnan, N., Nagaraja, H.N. (1992). A first course in order statistics. Wiley-Interscience, New York.Google Scholar
Artzner, P., Delbaen, F., Eber, J.M., Heath, D. (1999). Coherent measures of risk. Mathematical finance, 9(3), 203–228.CrossRefGoogle Scholar
Basel. (1988). International Convergence of Capital Measurement and Capital Standards. Basel Committee on Banking Supervision.Google Scholar
Basel. (1996). Amendment to the Capital Accord to Incorporate Market Risks. Basel Committee on Banking Supervision.Google Scholar
Basel. (2006). International Convergence of Capital Measurement and Capital Standards: A Revised Framework – Comprehensive Version. Basel Committee on Banking Supervision.Google Scholar
Basel Committee on Banking Supervision (2003). The 2002 Loss Data Collection Exercise for Operational Risk. Bank for International Settlements.Google Scholar
Basel Committee on Banking Supervision (2009). Results from the 2008 Loss Data Collection Exercise for Operational Risk Bank for International Settlements.Google Scholar
Baud, N., Frachot, A., Roncalli, T. (2002). Internal data, external data and consortium data for operational risk measurement: How to pool data properly?, 1–18. Groupe de Recherche Operationnelle, Credit Lyonnais, France.Google Scholar
Bühlmann, H., Shevchenko, P.V., Wüthrich, M.V. (2007). A “toy” model for operational risk quantification using credibility theory. Journal of Operational Risk, 2(1), 3–19.CrossRefGoogle Scholar
Cope, E., Labbi, A. (2008). Operational loss scaling by exposure indicators: Evidence from the ORX database. The Journal of Operational Risk, 3(4), 25–45.CrossRefGoogle Scholar
Dahen, H., Dionne, G. (2010). Scaling models for the severity and frequency of external operational loss data. Journal of Banking & Finance, 34(7), 1484–1496.Google Scholar
De Fontnouvelle, P., Dejesus-Rueff, V., Jordan, J.S., Rosengren, E.S. (2006). Capital and risk: New evidence on implications of large operational losses. Journal of Money, Credit, and Banking, 38(7), 1819–1846.CrossRefGoogle Scholar
De Fontnouvelle, P., Rosengren, E., Jordan, J. (2007). Chapter 10: Implications of Alternative Operational Risk Modeling Techniques. In M. Carey & R.M. Stulz (Eds.), The Risks of Financial Institutions (pp. 475–512). University of Chicago Press, Chicago.Google Scholar
Dunn, P.K., Smyth, G.K. (1996). Randomized Quantile Residuals. Journal of Computational and Graphical Statistics, 5(3), 236–244.Google Scholar
Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling extremal events for insurance and finance. Springer, Berlin: London.Google Scholar
Evans, J. (2001). Pitfalls in the Probability of Ruin Type Risk Management. Database of Actuarial Research Enquiry/Financial and Statistical Methods/Risk Pricing and Risk Evaluation Models/Probability of Ruin, Paper 30, pp. 501–510. Casualty Actuarial Society.Google Scholar
Gompers, P., Ishii, J., Metrick, A. (2003). Corporate governance and equity prices. The Quarterly Journal of Economics, 118(1), 107–155.CrossRefGoogle Scholar
Kupiec, P.H. (1995). Techniques for Verifying the Accuracy of Risk Management Models. Journal of Derivatives, 3(2), 73–84.Google Scholar
Lambrigger, D.D., Shevchenko, P.V., Wüthrich, M.V. (2007). The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions. The Journal of Operational Risk, 2(3), 3–27.Google Scholar
McNeil, A., Frey, R., Embrechts, P. (2005). Quantitative risk management: Concepts, techniques, and tools. Princeton University Press, New Jersey.Google Scholar
Medova, E.A., Berg-Yuen, P.E.K. (2009). Banking capital and operational risks: comparative analysis of regulatory approaches for a bank. Journal of Financial Transformation, 26, 85–96.Google Scholar
Moscadelli, M. (2004). The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee. Banca d'Italia.Google Scholar
Na, H., Van Den Berg, J., Miranda, L., Leipoldt, M. (2006). An econometric model to scale operational losses. The Journal of Operational Risk, 1(2), 11–31.Google Scholar
Nešlehová, J., Embrechts, P., Chavez-Demoulin, V. (2006). Infinite mean models and the LDA for operational risk. Journal of Operational Risk, 1(1), 3–25.CrossRefGoogle Scholar
R Development Core Team. (2010). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
Rigby, R.A., Stasinopoulos, D.M. (2001). The GAMLSS project: a flexible approach to statistical modelling. In B. Klein & L. Korsholm (Eds.), New Trends in Statistical Modelling: Proceedings of the 16th International Workshop on Statistical Modelling. Odense, Denmark.Google Scholar
Rigby, R.A., Stasinopoulos, D.M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3), 507–554.Google Scholar
Rigby, R.A., Stasinopoulos, D.M. (2010). A flexible regression approach using GAMLSS in R. http://gamlss.org/images/stories/papers/book-2010-Athens.pdf [accessed 30-Jul-2012].Google Scholar
Rootzén, H., Klüppelberg, C. (1999). A Single Number Can't Hedge against Economic Catastrophes. Ambio, 28(6), 550–555.Google Scholar
Shih, J., Khan, A.S., Medapa, P. (2000). Is the Size of an Operational Loss Related to Firm Size? Operational Risk Magazine, 2(1), 1–2.Google Scholar
Stasinopoulos, D.M., Rigby, R.A. (2007). Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, 23(7), 1–46.CrossRefGoogle Scholar
Ultsch, A. (2002). Proof of Pareto's 80/20 law and Precise Limits for ABC-Analysis. Technical Report 2002/c, DataBionics Reseach Group, University of Marburg.Google Scholar
Wei, R. (2007). Quantification of operational losses using firm-specific information and external database. Journal of Operational Risk, 1(4), 3–34.Google Scholar
Wilson, S. (2007). A Review of Correction Techniques for Inherent Biases in External Operational Risk Loss Data. Working Papers, Australian Prudential Regulation Authority.Google Scholar