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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.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 6 (February)
Pages: 3107-3127

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Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3107-3127
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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  1. 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.
  2. 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.
  3. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  4. 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.
  5. 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.
  6. repec:cup:cbooks:9780521405515 is not listed on IDEAS
  7. 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.
  8. repec:cup:cbooks:9780521477451 is not listed on IDEAS
  9. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  10. repec:cup:cbooks:9780521471626 is not listed on IDEAS
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