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.

Bayesian Copulae distributions, with application to Operational Risk management / L. Dalla Valle. - In: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY. - ISSN 1387-5841. - 11:1(2008 Mar), pp. 95-115. [10.1007/s11009-007-9067-x]

### Bayesian Copulae distributions, with application to Operational Risk management

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC) Bayesian normal copula; Bayesian Student's t copula; Expected shortfall; Loss distribution approach; Markov chain Monte Carlo;
Settore SECS-S/01 - Statistica
http://dx.doi.org/10.1007/s11009-007-9067-x
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/38851`
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