Loss Distribution Approach for Operational Risk

Abstract

In this paper, we explore the Loss Distribution Approach (LDA) for computing the capital charge of a bank for operational risk where LDA refers to statistical/actuarial methods for modelling the loss distribution. In this framework, the capital charge is calculated using a Value-at-Risk measure. In the first part of the paper, we give a detailed description of the LDA implementation and we explain how it could be used for economic capital allocation. In particular, we show how to compute the aggregate loss distribution by compounding the loss severity distribution and the loss frequency distribution, how to compute the total Capital-at-Risk using copulas, how to control the upper tail of the loss severity distribution with order statistics. In the second part of the paper, we compare LDA with the Internal Measurement Approach (IMA)proposed by the Basel Committee on Banking Supervision to calculate regulatory capital for operational risk. LDA and IMA are bottom - up internal measurement models which are apparently different. Nevertheless, we could map LDA into IMA and give then some justifications about the choice done by regulators to define IMA. Finally, we provide alternative ways of mapping both methods together.