This latest paper is a follow-up to Mr. BÃ¶ckerâs and Professor KlÃ¼ppelbergâs research paper published in the December 2005 issue of RISK, in which they presented a simple approximation of operational Value-at-Risk (âOpVaRâ) for a single operational risk cell. Their earlier body of work, entitled "Operational VaR: A Closed-form Approximation," demonstrated the ability to derive closed formulas for the calculation of univariate OpVaR at high confidence levels â an enhancement over commonly-used "black-box" simulation approaches to this issue since a closed formula generally allows for better analysis of the end result.
Mr. BÃ¶cker and Professor KlÃ¼ppelberg pursued their research in the context of Basel IIâs revised international framework for capital adequacy, which seeks to more closely align banksâ regulatory capital requirements with current and future risks. This revised framework allows for the increased use of internal bank risk assessments and quantification methods that incorporate individual banksâ market risk, credit risk and operational risk.
Consistent with the objectives of its revised framework, Basel II introduced the Advanced Measurement Approaches (AMA) for assessing operational risk. Banks choosing to use an AMA to calculate the regulatory capital charge for operational risk must receive prior approval for a comprehensive operational risk measurement system that incorporates methods, instruments, IT systems, and review, control and monitoring processes.
Basel II explicitly refers to the issue of correlation (or more generally, the dependence structure among different operational risk estimates), which might result in a diversification benefit and an eventual reduction in overall operational risk. In âMultivariate Models for Operational Risk,â Mr. BÃ¶cker and Professor KlÃ¼ppelberg tackled this problem and investigated how such a dependence structure could be modeled using the novel concept of a LÃ©vy copula. By using LÃ©vy copulas, the researchers were able to derive closed-form approximations for important examples of heavy-tailed loss severity distributions and dependence structures.
The LÃ©vy copula draws on the general theory of LÃ©vy stochastic processes, which can be applied to loss distribution concepts employed in the actuarial profession, as well as to operational risk. Use of the LÃ©vy copula in this context is an innovative, intuitive approach with significant benefits for enterprise risk management.
The awarded paper has been widely recognized for its contribution to analyzing the behavior of multivariate operational risk. It has been received very favorably in the regulatory and risk management communities, including Deutsche Bundesbank and delegates to the Risk Capital Conference in Paris in 2006. These and other practitioners are very interested in the fact that closed-formula results for OpVaR can often be applied to estimate OpVaR with a low approximation error.
The co-authors look forward to the prospect of applying their generalized model of multivariate behavior to actual internal bank data for statistical estimations and parameterizing a LÃ©vy copula in practice. They are particularly interested in seeing the LÃ©vy copula becoming more popular in the assessment of operational risk and enterprise risk management in general.
Dr. Dan Oprescu, head of the Risk Management Practice for Financial Architects N.V. (FinArch) and a recognized expert in the field of Enterprise Risk Management, was a member of the selection committee for the PRMIA Institute award. In Dr. Oprescuâs words, the BÃ¶cker- KlÃ¼ppelberg paper stood out among its peers for its theoretical contributions to the analysis of ERM by âproposing a new framework that could unify the modelling of different types of event risk â a very important challenge faced by enterprise-wide risk models today. The paper presents the framework in a mathematically consistent fashion and then investigates some of its likely applications, showing risk modellers and managers how the framework could be adapted to individual circumstances.â