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A Bayesian approach to estimate the marginal loss distributions in operational risk management


  • Dalla Valle, L.
  • Giudici, P.


One of the main problems in operational risk management is the lack of loss data, which affects the parameter estimates of the marginal distributions of the losses. The principal reason is that financial institutions only started to collect operational loss data a few years ago, due to the relatively recent definition of this type of risk. Considering this drawback, the employment of Bayesian methods and simulation tools could be a natural solution to the problem. The use of Bayesian methods allows us to integrate the scarce and, sometimes, inaccurate quantitative data collected by the bank with prior information provided by experts. An original proposal is a Bayesian approach for modelling operational risk and for calculating the capital required to cover the estimated risks. Besides this methodological innovation a computational scheme, based on Markov chain Monte Carlo simulations, is required. In particular, the application of the MCMC method to estimate the parameters of the marginals shows advantages in terms of a reduction of capital charge according to different choices of the marginal loss distributions.

Suggested Citation

  • Dalla Valle, L. & Giudici, P., 2008. "A Bayesian approach to estimate the marginal loss distributions in operational risk management," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3107-3127, February.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3107-3127

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    References listed on IDEAS

    1. Jacques Pezier, 2002. "A Constructive Review of Basel's Proposals on Operational Risk," ICMA Centre Discussion Papers in Finance icma-dp2002-20, Henley Business School, Reading University.
    2. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, April.
    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. Kühn, Reimer & Neu, Peter, 2003. "Functional correlation approach to operational risk in banking organizations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 650-666.
    5. Cornalba, Chiara & Giudici, Paolo, 2004. "Statistical models for operational risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 166-172.
    6. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk (3): Their Validity under Market Stress," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(3), pages 181-237, October.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
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    Cited by:

    1. Paola Cerchiello & Paolo Giudici, 2016. "How to measure the quality of financial tweets," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(4), pages 1695-1713, July.
    2. Fantazzini, Dean, 2008. "Econometric Analysis of Financial Data in Risk Management (continuation). Section III: Managing Operational Risk," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 11(3), pages 87-122.
    3. Paola Cerchiello & Paolo Giudici, 2013. "H Index: A Statistical Proposal," DEM Working Papers Series 039, University of Pavia, Department of Economics and Management.
    4. repec:spr:scient:v:99:y:2014:i:2:d:10.1007_s11192-013-1194-2 is not listed on IDEAS
    5. Paolo Giudici, 2015. "Scorecard models for operations management," International Journal of Data Science, Inderscience Enterprises Ltd, vol. 1(1), pages 96-101.
    6. Otranto, Edoardo, 2008. "Clustering heteroskedastic time series by model-based procedures," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4685-4698, June.
    7. Silvia Figini & Lijun Gao & Paolo Giudici, 2013. "Bayesian operational risk models," DEM Working Papers Series 047, University of Pavia, Department of Economics and Management.
    8. Lu, Zhaoyang, 2011. "Modeling the yearly Value-at-Risk for operational risk in Chinese commercial banks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 604-616.
    9. Paola Cerchiello & Paolo Giudici, 2015. "A Bayesian h-index: how to measure research impact," DEM Working Papers Series 102, University of Pavia, Department of Economics and Management.

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