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Scaling Models for the Severity and Frequency of External Operational Loss Data


  • Hela Dahen
  • Georges Dionne


According to Basel II criteria, the use of external data is absolutely indispensable to the implementation of an advanced method for calculating operational capital. This article investigates how the severity and frequencies of external losses are scaled for integration with internal data. We set up an initial model designed to explain the loss severity. This model takes into account firm size, location, and business lines as well as risk types. It also shows how to calculate the internal loss equivalent to an external loss, which might occur in a given bank. OLS estimation results show that the above variables have significant power in explaining the loss amount. They are used to develop a normalization formula. A second model based on external data is developed to scale the frequency of losses over a given period. Two regression models are analyzed: the truncated Poisson model and the truncated negative binomial model. Variables estimating the size and geographical distribution of the banks' activities have been introduced as explanatory variables. The results show that the negative binomial distribution outperforms the Poisson distribution. The scaling is done by calculating the parameters of the selected distribution based on the estimated coefficients and the variables related to a given bank. Frequency of losses of more than $1 million are generated on a specific horizon.

Suggested Citation

  • Hela Dahen & Georges Dionne, 2007. "Scaling Models for the Severity and Frequency of External Operational Loss Data," Cahiers de recherche 0702, CIRPEE.
  • Handle: RePEc:lvl:lacicr:0702

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    References listed on IDEAS

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    Cited by:

    1. Eckert, Christian & Gatzert, Nadine, 2017. "Modeling operational risk incorporating reputation risk: An integrated analysis for financial firms," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 122-137.
    2. Häger, David & Andersen, Lasse B., 2010. "A knowledge based approach to loss severity assessment in financial institutions using Bayesian networks and loss determinants," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1635-1644, December.
    3. Zhou, Xiaoping & Durfee, Antonina V. & Fabozzi, Frank J., 2016. "On stability of operational risk estimates by LDA: From causes to approaches," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 266-278.
    4. Valérie Chavez-Demoulin & Paul Embrechts & Marius Hofert, 2016. "An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 735-776, September.
    5. Cope, Eric W. & Piche, Mark T. & Walter, John S., 2012. "Macroenvironmental determinants of operational loss severity," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1362-1380.
    6. Fiordelisi, Franco & Soana, Maria-Gaia & Schwizer, Paola, 2013. "The determinants of reputational risk in the banking sector," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1359-1371.
    7. Dániel Homolya, 2016. "Risk Management Approaches and Bank Size," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 15(2), pages 114-128.
    8. Jose Manuel Feria-Dominguez & Enrique Jimenez-Rodriguez & Pilar Camacho-Rubio, 2014. "People Value at Risk: A Key Indicator for Sound Management," Working Papers 14.03, Universidad Pablo de Olavide, Department of Financial Economics and Accounting (former Department of Business Administration).
    9. Rangga Handika & Chi Truong & Stefan Trueck & Rafal Weron, 2014. "Modelling price spikes in electricity markets - the impact of load, weather and capacity," HSC Research Reports HSC/14/08, Hugo Steinhaus Center, Wroclaw University of Technology.
    10. Pupashenko, Daria & Ruckdeschel, Peter & Kohl, Matthias, 2015. "L2 differentiability of generalized linear models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 155-164.
    11. Mizgier, Kamil J. & Hora, Manpreet & Wagner, Stephan M. & Jüttner, Matthias P., 2015. "Managing operational disruptions through capital adequacy and process improvement," European Journal of Operational Research, Elsevier, vol. 245(1), pages 320-332.
    12. Amandha Ganegoda & John Evans, 2014. "A framework to manage the measurable, immeasurable and the unidentifiable financial risk," Australian Journal of Management, Australian School of Business, vol. 39(1), pages 5-34, February.
    13. Feria-Domínguez, José Manuel & Jiménez-Rodríguez, Enrique & Sholarin, Ola, 2015. "Tackling the over-dispersion of operational risk: Implications on capital adequacy requirements," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 206-221.
    14. Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013. "The Risk Map: A new tool for validating risk models," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3843-3854.
    15. Suren Pakhchanyan, 2016. "Operational Risk Management in Financial Institutions: A Literature Review," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 4(4), pages 1-21, October.
    16. Georges Dionne & Amir Saissi Hassani, 2015. "Endogenous Hidden Markov Regimes in Operational Loss Data: Application to the Recent Financial Crisis," Cahiers de recherche 1516, CIRPEE.
    17. Chernobai, Anna & Ozdagli, Ali K. & Wang, Jianlin, 2016. "Business complexity and risk management: evidence from operational risk events in U. S. bank holding companies," Working Papers 16-16, Federal Reserve Bank of Boston.

    More about this item


    Operational risk in banks; scaling; severity distribution; frequency distribution; truncated count data regression models;

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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