Evaluating operational risk by an inhomogeneous counting process based on Panjer recursion

José Alfredo Jiménez and Viswanathan Arunachalam

Abstract

ABSTRACT

Operational risk (OpRisk) is increasingly being considered an important financial risk. In recent years, it has been given more consideration due to economically disturbing events. The loss distribution approach (LDA) is one of the demanding models suggested by the Basel Committee on Banking Supervision (BCBS). The purpose of this paper is to propose a new approach for determining operational value-at-risk (OpVaR) using an inhomogeneous counting process based on Panjer recursion as the frequency distribution, and generalized Pareto distributions and generalized extreme value distributions are used to model the severities. We focus on the inhomogeneous Panjer process (IPP) and investigate its properties. In this paper, we present the LDA for computing OpRisk using IPP. The closed-form expression for the moment generating function for determining the aggregate loss distribution is derived. We generalize well-known classical models and derive the statistical characteristics for modeling loss distribution. An illustration is presented to demonstrate the applicability of the proposed model in OpRisk and also discuss various special cases of the model.