Operational risk quantified with spectral risk measures: a refined closed-form approximation. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Tong, Bin; Diao, Xundi; Wu, Chongfeng
• Is Part Of: Quantitative finance. Volume 19:Issue 7(2019)
• Page Start: 1221
• Page End: 1242
• Publication Date: 2019-07-03
• Subjects: Operational risk -- Spectral risk measures -- Regular variation -- Second-order regular variation -- Asymptotically smooth -- Second-order subexponentiality; C14 -- C16 -- C65 -- G21; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2018.1564066
• Languages: English
• ISSNs: 1469-7688

Abstract

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.