First‐Order Approximations to Operational Risk: Dependence and Consequences

Abstract

We investigate the problem of modelling and measuring multidimensional operational risk.Based on the very popular univariate loss distribution approach, we suggest an "invariance principle" which should be satisfied by any multidimensional operational risk model, and which is naturally fulfilled by our modelling technique based on the new concept of Pareto Lévy copulas. Our approach allows for a fully dynamic modelling of operational risk at any future point in time. We exploit the fact that operational loss data are typically heavy-tailed, and, therefore, we intensively discuss the concept of multivariate regular variation, which is considered as a very useful tool for various multivariate heavy-tailed phenomena. Moreover, for important examples of the Pareto Lévy copulas and appropriate severity distributions we derive first order approximations for multivariate operational Value-at-Risk.

Do operational risk and corporate governance affect the banking industry of Pakistan?

“…ORM initiated with its identification. Bocker and Kluppelberg (2005) suggest that the only feasible way to manage operational risk successfully is by identifying and minimizing it, which requires the development of adequate quantification techniques. It is a challenging issue to identify operational risk, as the factors of operational risk are not well defined (Muermann and Oktem, 2002).…”

Nonparametric inference on Lévy measures and copulas

“…On the other hand, since the (Pareto) Lévy copula captures the tendency of the process to have joint (largely negative) jumps, the need for reliable nonparametric estimators is evident from practice, particularly with a view on finance. See, for instance, Böcker and Klüppelberg (2009) who model operational risk via Pareto-Lévy copulas. This convinces us that there is a clear gap in the literature which we aim to fill in this work.…”

Modeling Correlations in Operational Risk

“…Our numerical results showed that the proposed method is efcient in comparison to a simple summation simulations for computing tail loss probabilities and conditional expectations. We also compared the proposed method with another reference model based on the ParetoLévy copulas [3,5]. On this basis it can be stated that the proposed algorithm gives promising results.…”

“…Correlation modeled by T-copulas; The ParetoLévy copulas model, which was used as a benchmark [3,5].…”

“…They allow for description of more complex dependences between variables than the Pearson correlation and can be implemented in the Monte Carlo framework used in LDA [15]. Therefore copulas have been frequently used to model dependences in operational risk [3,5,16,17]. …”