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.

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people or systems, or from external events. The New Basel Capital Accord (BCBS, 2004) emphasizes the quantification and management of operational risk because of its pervasive nature. The proposed methods for operational risk quantification are: Basic Indicator Approach, Standardized Approach and Advanced Measurement Approach (AMA), which includes Loss Distribution Approach (LDA) and Scenario-Based Approach. Among these methods, LDA measures operational risk capital based on bank's own historical loss data of least five years. LDA involves two types of distribution fitting and analysis, which are severity and frequency distribution, and then loss distribution is generated employing mathematical convolution, usually conducted by Monte-Carlo simulation in practice. There is a 7 * 8 operational loss data matrix for LDA, where 7 denotes types of loss events and 8 denotes business lines. The atomic unit for the calculation of operational risk capital is a specific cell of the 7 * 8 matrix. To quantify bank-wide operational risk capital, we need to model the dependence among cell by cell loss distributions employing statistical methodology. For this purpose, we should consider the source of dependence of bank-wide aggregate loss distribution. In this paper, we focus on the dependence among loss frequencies of the cells of the 7 * 8 matrix and propose how to generate bank-wide loss distribution considering the frequency dependence.

Financial Risk Management Journal, Advanced Measurement Approach, AMA, Loss Distribution Approach LDA, Operational Risk Matrix, Marginal Loss Distribution, Statistical Methodology, Correlation Matrix, Linear Correlation, Mathematical Convolution, Marginal Distribution, Operational Capital, Marginal Loss.