Abstract
The management of Operational Risk has been a difficult task due to the lack of data and the high number of variables. In this project, we treat operational risks as multivariate variables. In order to model them, copula functions are employed, which are a widely used tool in finance and engineering for building flexible joint distributions. The purpose of this research is to propose a new methodology for modelling Operational Risks and estimating the required capital. It combines the use of graphical models and the use of copula functions along with hyper-Markov law. Historical loss data of an Italian bank is used, in order to explore the methodology’s behaviour and its potential benefits.
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References
Alexander C (2003) Operational risk. Financial Prentice Hall, London
Artzner P, Delbaen F, Eber J, Heath D (1999) Coherent measures of risk. Mathematical Finance 9(3):203–228
Cornalba C, Giudici P (2004) Statistical models for operational risk management. Physica A 338:166–172
Cowell RG, Dawid AP, Lauritzen SL, Spiegelhalter DJ (1999) Probabilistic networks and expert systems, series: statistics for engineering and information science. Springer, New York
Cruz M (2004) Operational risk modelling and analysis: theory and practice. Bharat Book Bureau
Dalla Valle L, Fantazzini D, Giudici P (2005) Copula and operational risks, (contact Dalla Valle L. at luciana.dallavalle@unimib.it)
Dawid AP, Lauritzen SL (1993) Hyper Markov Law is the statistical analysis of decomposable graphical models. Ann Stat 21(3):1272–1317 Sept
Giudici P, Bilotta A (2004) Modelling operational losses: a Bayesian approach. Quality and Reliability Engineering International 20(5):407–417
Jensen FV (2001) Bayesian networks and decision graphs, series: statistics for engineering and information science. Springer, New York
Jordan MI (1999) Learning in graphical models. MIT Press, Cambridge
Murphy KP (2001) An introduction to graphical models, available at www.ai.mit.edu/murphyk/papers.html, May 10
Neapolitan RE (2004) Learning Bayesian networks. Pearson Prentice Hall Series in Artificial Intelligence, edition
Nelsen RB (1999) An introduction to Copulas, Lecture Notes in Statistics 139, Springer, New York
Romano C (2002) Calibrating and simulating copula functions: an application to the Italian stock market, available at http://www.gloriamundi.org
Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publ Inst Stat Univ Paris 8:229–231
Sklar A (1996) Random variables, distribution functions and copulas—a personal look backward and forward. In: Rüschendorff L, Schweitzer B, Taylor M (eds) Distributions with fixed marginals and related topics. Institute of Mathematical Statistics, Hayward, pp 1–14
Yamai Y, Yoshiba T (2002) Comparative analyses of expected shortfall and value-at-risk: their validity under market stress. Monetary and Economic Studies 20:181–238 Oct
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Politou, D., Giudici, P. Modelling Operational Risk Losses with Graphical Models and Copula Functions. Methodol Comput Appl Probab 11, 65–93 (2009). https://doi.org/10.1007/s11009-008-9083-5
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DOI: https://doi.org/10.1007/s11009-008-9083-5