Asymptotics for operational risk quantified with a spectral risk measure

Bin Tong and Chongfeng Wu

Abstract

ABSTRACT

The measurement and management of operational risk has become an increasingly important issue as a result of the new capital requirement for operational risk implemented in the New Basel Capital Accord (Basel II). We deal with asymptotic results for operational risk quantified with a spectral risk measure for a single cell as the confidence level converges to 100%. Following the work of Böcker and Klüppelberg and Biagini and Ulmer in their papers of 2010 and 2009, respectively, we also extend the related results to multivariate case, where the dependence structure between different cells is characterized by a Lévy copula. We derive first-order asymptotic results for the operational spectral risk measure in various dependence scenarios. The asymptotic results documented in this study may give further insights into the quantification of operational risk, and may be of interest to managers, policy makers and scholars.