Operational risk modeling under the loss distribution approach

Abstract

The term operational risk became widespread in the late 1990s when central bank representatives of twelve countries formed a working committee; the Basel Committee on Banking Supervision (BCBS). The BCBS defines operational risk as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This research aims to model operational risk data using the Loss Distribution Approach under BCBS requirements. Simulated data was used consisting of 3,192 operational loss events between the years 2009 and 2018. The implementation of the LDA was conducted using R programming language; R studio 4.0.3. Due to the low count of loss events, the LDA could not be implemented at business line-risk category levels. Rather, it was implemented per business line and a second time per risk category. The capital requirement was determined for each case. Loss frequency and severity distributions were modeled, the aggregate loss distribution was determined through convolution, and finally the overall distribution was obtained through a copula function. Capital requirements were calculated for each year as the difference between the 99.9% VaR and the Expected Loss (EL). Significant differences were identified between the yearly capital requirements obtained for each of the two cases. Since operational risk data encompasses high-frequency low-severity and low- frequency high-severity events, the variations of gross loss amounts within business lines and risk categories have a huge impact on the capital requirement. As per Basel requirements, internally generated operational risk measures used for regulatory capital purposes must be based on a minimum five-year observation period of internal loss data. Therefore, the total 10 year period was considered and a weighted average of the capital charge was calculated. Both cases yielded rather close capital charges. The business line method recorded a lower capital charge by around 15%. Ultimately, and to diminish the impact of operational risk, the larger capital charge of 8,738,614$ is recommended for the next year. The impact of the research findings is correlated towards a better understanding of the composition and distribution of operational risk data over risk classes and the corresponding operational risk capital requirements.