×

Modelling operational risk losses with graphical models and copula functions. (English) Zbl 1293.90078

Summary: 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.

MSC:

90C40 Markov and semi-Markov decision processes
91G40 Credit risk
91B30 Risk theory, insurance (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alexander C (2003) Operational risk. Financial Prentice Hall, London
[2] Artzner P, Delbaen F, Eber J, Heath D (1999) Coherent measures of risk. Mathematical Finance 9(3):203–228 · Zbl 0980.91042 · doi:10.1111/1467-9965.00068
[3] Cornalba C, Giudici P (2004) Statistical models for operational risk management. Physica A 338:166–172 · doi:10.1016/j.physa.2004.02.039
[4] Cowell RG, Dawid AP, Lauritzen SL, Spiegelhalter DJ (1999) Probabilistic networks and expert systems, series: statistics for engineering and information science. Springer, New York
[5] Cruz M (2004) Operational risk modelling and analysis: theory and practice. Bharat Book Bureau
[6] Dalla Valle L, Fantazzini D, Giudici P (2005) Copula and operational risks, (contact Dalla Valle L. at luciana.dallavalle@unimib.it)
[7] Dawid AP, Lauritzen SL (1993) Hyper Markov Law is the statistical analysis of decomposable graphical models. Ann Stat 21(3):1272–1317 Sept · Zbl 0815.62038 · doi:10.1214/aos/1176349260
[8] Giudici P, Bilotta A (2004) Modelling operational losses: a Bayesian approach. Quality and Reliability Engineering International 20(5):407–417 · doi:10.1002/qre.655
[9] Jensen FV (2001) Bayesian networks and decision graphs, series: statistics for engineering and information science. Springer, New York
[10] Jordan MI (1999) Learning in graphical models. MIT Press, Cambridge
[11] Murphy KP (2001) An introduction to graphical models, available at www.ai.mit.edu/murphyk/papers.html , May 10
[12] Neapolitan RE (2004) Learning Bayesian networks. Pearson Prentice Hall Series in Artificial Intelligence, edition
[13] Nelsen RB (1999) An introduction to Copulas, Lecture Notes in Statistics 139, Springer, New York · Zbl 0909.62052
[14] Romano C (2002) Calibrating and simulating copula functions: an application to the Italian stock market, available at http://www.gloriamundi.org
[15] Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publ Inst Stat Univ Paris 8:229–231 · Zbl 0100.14202
[16] 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
[17] 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 · Zbl 1080.91047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.