Measuring Tail Operational Risk in Univariate and Multivariate Models with Extreme Losses

28 Pages Posted: 22 Mar 2023

See all articles by Yang Yang

Yang Yang

School of Statistics and Mathematics, Nanjing Audit University; Nanjing Audit University

Yishan Gong

Xi'an University of Finance and Economics; Xi'an Jiaotong-Liverpool University (XJTLU)

Jiajun Liu

Xi'an Jiaotong-Liverpool University

Date Written: March 21, 2022

Abstract

This paper considers some univariate and multivariate operational risk models, in which the loss severities are modeled by some weakly tail dependent and heavy-tailed positive random variables, and the loss frequency processes are some general counting processes. We derive some limit behaviors for the value-at-risk and conditional tail expectation of aggregate operational risks in such models. The methodology is based on capital approximation within the Basel II/III framework (the so-called loss distribution approach). We also conduct some simulation studies to check the accuracy of our approximations and the (in)sensitivity due to different dependence structures or to the heavy-tailedness of the severities.

Keywords: asymptotics, operational risk, value-at-risk (VaR), conditional tail expectation (CTE), asymptotic independence, regular variation

Suggested Citation

Yang, Yang and Gong, Yishan and Liu, Jiajun, Measuring Tail Operational Risk in Univariate and Multivariate Models with Extreme Losses (March 21, 2022). Journal of Operational Risk, Vol. 18, No. 1, 2023, Available at SSRN: https://ssrn.com/abstract=4395241

Yang Yang (Contact Author)

School of Statistics and Mathematics, Nanjing Audit University

Nanjing Audit University ( email )

Minxing Building,86 West Yushan Road, Pukou Distr
Nanjing, Jiangsu
China

Yishan Gong

Xi'an University of Finance and Economics

Xi'an Jiaotong-Liverpool University (XJTLU)

Jiajun Liu

Xi'an Jiaotong-Liverpool University ( email )

111 Renai Road, SIP
, Lake Science and Education Innovation District
Suzhou, JiangSu province 215123
China
+86 81884732 (Phone)

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