Bayesian Copulae Distributions, with Application to Operational Risk Management

• C. Acerbi, and D. Tasche, “On the coherence of expected shortfall,” Journal of Banking and Finance, vol. 26 pp. 1487–1503, 2002.

  Article  Google Scholar 

• C. Alexander, Operational Risk. Regulation, Analysis and Management, Alexander (ed.), Financial Times Prentice Hall: London, 2003.

  Google Scholar 

• V. Arakelian, and P. Dellaportas Contagion tests via copula threshold models, Working Paper, University of Athens, 2006.

• P. Artzner, F. Delbaen, J. Eber, and D. Heath, “Coherent measures of risk,” Mathematical Finance vol. 9(3) pp. 203–228, 1999.

  Article  MATH  MathSciNet  Google Scholar 

• M. C. Ausin, and H. F. Lopes, Time-varying joint distribution through copulas, Working paper, Univesity of Chicago, 2006.

• Basel Commitee on Banking Supervision, Basel II: the New Basel Capital Accord. Second Consultantive Paper. Report to the Bank for International Settlements. Available at http://www.bis.org. 2001.

• Basel Commitee on Banking Supervision, Basel II: the New Basel Capital Accord. Third Consultantive Paper, Report to the Bank for International Settlements. Available at http://www.bis.org. 2003.

• J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd ed., Springer-Verlag: New York, 1985.

  MATH  Google Scholar 

• J. M. Bernardo, and A. F. M. Smith, Bayesian Theory, Wiley: Chichester, 1994.

  Book  MATH  Google Scholar 

• S. P. Brooks, “Markov chain monte carlo method and its application”, The Statistician, no. 47, Part 1, pp. 69–100, 1997.

  Google Scholar 

• X. Chen, Y. Fan, and A. J. Patton, Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates, London Economics Financial Markets Group Working Paper No. 483, 2004.

• M. Cruz, Modeling, Measuring and Hedging Operational Risk, Wiley: Chichester, 2002.

  Google Scholar 

• L. Dalla Valle, Statistical Models for Enterprise Risk Evaluation, PhD dissertation, 2007.

• L. Dalla Valle, and P. Giudici, A Bayesian Approach to estimate the Marginal loss distributions in Operational Risk Management, Working Paper, University of Pavia, 2007.

• L. Dalla Valle, D. Fantazzini, and P. Giudici, “Copulae and operational risk,” International Journal of Risk Assessment and Management, forthcoming, 2008.

• P. Dellaportas, and I. Papageorgiou, “Multivariate mixtures of normals with unknown number of components,” Statistics and Computing, vol. 16(1) pp. 57–68, 2006.

  Article  MathSciNet  Google Scholar 

• A. Frachot, P. Georges, and T. Roncalli, Loss distribution approach for operational risk. Groupe de Recherche Opérationnelle du Crédit Lyonnais. Working Paper, 2001.

• D. Gamerman, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman and Hall: London, 1997.

  MATH  Google Scholar 

• A. E. Gelfand, and A. F. M. Smith, “Sampling based approaches to calculating marginal densities,” Jounal of American Statistical Association, n. 85, pp. 398–409, 1990.

  Article  MATH  MathSciNet  Google Scholar 

• P. Giudici, and P. J. Green, “Decomposable graphical Gaussian model determination,” Biometrica, vol. 86(4) pp. 785–801, 1999.

  Article  MATH  MathSciNet  Google Scholar 

• W. K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika, n. 57 pp. 97–109, 1970.

  Article  MATH  Google Scholar 

• H. Joe, Multivariate Models and Dependence Concepts, Chapman Hall: London, 1997.

  MATH  Google Scholar 

• S. Kotz, N. Balakrishnan, and N. L. Johnson, Continuous multivariate distributions, volume 1. 2nd edn, Models and applications, New York, John Wiley & Sons, 2000.

  Book  Google Scholar 

• R. Kuhn, and P. Neu, “Functional correlation approach to operational risk in banking organizations,” Physica A, vol. 322 pp. 650–666, 2003.

  Article  Google Scholar 

• E. L. Lehmann, and G. Casella, Theory of Poit Estimation, revised ed. Springer-Verlag: New York, 1998.

  Google Scholar 

• N. Metropolis, A. N. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculation by fast computing machine,” Journal of Chemical Physics, vol. 21(6) pp. 1087–1092, 1953.

  Article  Google Scholar 

• R. Nash, “The three pillars of operational risk.” In Alexander (ed.), Operational risk. Regulation, analysis and management, Financial Times Prentice Hall: London, 2003.

  Google Scholar 

• R. B. Nelsen, An Introduction to Copulas, Lecture Notes in Statistics 139, Springer: New York, 1999.

  Google Scholar 

• J. Pezier, A Constructive Review of the Basel Proposals on Operational Risk, ISMA Discussion Papers in Finance, University of Reading, 2002.

• M. Pitt, D. Chan, and R. Kohn, “Efficient Bayesian inference for Gaussian copula regression models,” Biometrika, vol. 93(3) pp. 537–554, 2006.

  Article  MATH  MathSciNet  Google Scholar 

• B. D. Ripley, Stochastic Simulation, Wiley: London, 1987.

  Book  MATH  Google Scholar 

• Risk Management Group, The 2002 Loss Data Collection Exercise for Operational Risk: Summary of the Data Collected, Report to the Basel Committee on Banking Supervision, Bank for International Settlements. Available at http://www.bis.org. 2003.

• C. Robert, “Convergence assesments for Markov chain Monte Carlo methods,” Statistical Science, n. 10 pp. 231–253, 1996.

  Article  Google Scholar 

• C. P. Robert, and G. Casella, Monte Carlo Statistical Methods, Springer: New York, 1999.

  MATH  Google Scholar 

• C. Romano, Applying copula functions to risk management, Working paper, University of Rome “La Sapienza”, 2001.

• A. Sklar, “Fonctions de rt’epartition ‘a n dimensionset leurs marges,” Publications de l’Institut de statistique de l’Universite de Paris, n. 8 pp. 229–231, 1959.

  MathSciNet  Google Scholar 

• Y. Yamai, and T. Yoshiba, “Comparative analyses of expected shortfall and value-at-risk: Their validity under market stress,” Monetary and Economic Studies, pp. 181–238, 2002.

• Y. Yasuda, Application of Bayesian Inference to Operational Risk Management, University of Tsukuba, 2003.

Download references