A Study on the Dependence Structure of Aggregate Loss Distributions Based on Frequency Dependence

The dependence structure among cell by cell in operational risk matrix is a critical issue in the determination of bank-wide operational risk capital under Advanced Measurement Approach (AMA). Especially, Loss Distribution Approach (LDA), which is one of the main methods in AMA, involves statistical inference on the frequency and severity distribution, and then loss distribution is generated via Monte-Carlo simulation. This procedure is conducted based on a specific cell in the operational risk matrix whose dimension is 7 * 8 in AMA. To generate bank-wide operational loss distribution, dependence structure among cell by cell loss distribution has to be modeled in a consistent manner. This paper proposes a methodology for generating firm-wide loss distribution based on frequency dependence, which is a primary source of the dependence structure. It especially highlights how to model the frequency dependence of loss distribution via copula, which is a function that links marginal and joint distributions. The main contribution of this paper is that it provides a very flexible method for modeling the dependence of individual loss distribution, and it is confirmed that the proposed method is satisfied in terms of conservatism. The study finds that bank-wide capital increases at about 15% as the dependence becomes stronger, and this empirical result is consistent with changes in the severity distribution of marginal loss distributions