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Bayesian Copulae Distributions, with Application to Operational Risk Management

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  • Luciana Dalla Valle

    (University of Milan)

Abstract

The aim of this paper is to introduce a new methodology for operational risk management, based on Bayesian copulae. One of the main problems related to operational risk management is understanding the complex dependence structure of the associated variables. In order to model this structure in a flexible way, we construct a method based on copulae. This allows us to split the joint multivariate probability distribution of a random vector of losses into individual components characterized by univariate marginals. Thus, copula functions embody all the information about the correlation between variables and provide a useful technique for modelling the dependency of a high number of marginals. Another important problem in operational risk modelling is the lack of loss data. This suggests the use of Bayesian models, computed via simulation methods and, in particular, Markov chain Monte Carlo. We propose a new methodology for modelling operational risk and for estimating the required capital. This methodology combines the use of copulae and Bayesian models.

Suggested Citation

  • Luciana Dalla Valle, 2009. "Bayesian Copulae Distributions, with Application to Operational Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 95-115, March.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:1:d:10.1007_s11009-007-9067-x
    DOI: 10.1007/s11009-007-9067-x
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
    2. Philipp Arbenz, 2013. "Bayesian Copulae Distributions, with Application to Operational Risk Management—Some Comments," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 105-108, March.
    3. Juan Wu & Xue Wang & Stephen G. Walker, 2014. "Bayesian Nonparametric Inference for a Multivariate Copula Function," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 747-763, September.
    4. Shumin Ma & Zhiri Yuan & Qi Wu & Yiyan Huang & Xixu Hu & Cheuk Hang Leung & Dongdong Wang & Zhixiang Huang, 2023. "Deep into The Domain Shift: Transfer Learning through Dependence Regularization," Papers 2305.19499, arXiv.org.
    5. Fantazzini, Dean, 2008. "Econometric Analysis of Financial Data in Risk Management (continuation). Section III: Managing Operational Risk," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 11(3), pages 87-122.
    6. Tahani S. Alotaibi & Luciana Dalla Valle & Matthew J. Craven, 2022. "The Worst Case GARCH-Copula CVaR Approach for Portfolio Optimisation: Evidence from Financial Markets," JRFM, MDPI, vol. 15(10), pages 1-14, October.
    7. Luca Regis, 2011. "A Bayesian copula model for stochastic claims reserving," Carlo Alberto Notebooks 227, Collegio Carlo Alberto.
    8. Rada Dakovic & Claudia Czado, 2011. "Comparing point and interval estimates in the bivariate t-copula model with application to financial data," Statistical Papers, Springer, vol. 52(3), pages 709-731, August.
    9. Pavel V. Shevchenko, 2009. "Implementing Loss Distribution Approach for Operational Risk," Papers 0904.1805, arXiv.org, revised Jul 2009.
    10. Mohamed Habachi & Saâd Benbachir, 2020. "The Bayesian Approach to Capital Allocation at Operational Risk: A Combination of Statistical Data and Expert Opinion," IJFS, MDPI, vol. 8(1), pages 1-25, February.

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