Journal of Operational Risk

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

José Alfredo Jiménez and Viswanathan Arunachalam

  • The paper studies the Panjer counting process as a frequency distribution for modeling OpRisk.
  • Some special kind of severity distribution such as the Tukey's g-h distribution is considered.
  • An explicit expressions for the moment generating function for calculating the aggregate loss is derived.
  • The paper contains an empirical data in which statistics of operational risk are described.


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.

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