Operational risk quantified with spectral risk measures: a refined closed-form approximation

Bin Tong, Xundi Diao and Chongfeng Wu

Quantitative Finance, 2019, vol. 19, issue 7, 1221-1242

Abstract: The quantification of operational risk has become an important issue as a result of the new capital charges required by the Basel Capital Accord (Basel II) to cover the potential losses of this type of risk. In this paper, we investigate second-order approximation of operational risk quantified with spectral risk measures (OpSRMs) within the theory of second-order regular variation (2RV) and second-order subexponentiality. The result shows that asymptotically two cases (the fast convergence case and the slow convergence) arise depending on the range of the second-order parameter. We also show that the second-order approximation under 2RV is asymptotically equivalent to the slow convergence case. A number of Monte Carlo simulations for a range of empirically relevant frequency and severity distributions are employed to illustrate the performance of our second-order results. The simulation results indicate that our second-order approximations tend to reduce the estimation errors to a great degree, especially for the fast convergence case, and are able to capture the sub-extremal behavior of OpSRMs better than the first-order approximation. Our asymptotic results have implications for the regulation of financial institutions, and may provide further insights into the measurement and management of operational risk.

Date: 2019
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DOI: 10.1080/14697688.2018.1564066

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