Using a time series approach to correct serial correlation in operational risk capital calculation

The advanced measurement approach requires financial institutions to develop internal models to evaluate regulatory capital. Traditionally, the loss distribution approach (LDA) is used, mixing frequencies and severities to build a loss distribution function (LDF). This distribution represents annual losses; consequently, the 99.9th percentile of the distribution providing the capital charge denotes the worst year in a thousand. The traditional approach approved by the regulator and implemented by financial institutions assumes the losses are independent. This paper proposes a solution to address the issues arising when autocorrelations are detected between the losses, by using time series. Thus, the losses are aggregated periodically and several models are adjusted using autoregressive models, autoregressive fractionally integrated and Gegenbauer processes considering various distributions fitted on the residuals. Monte Carlo simulation enables the construction of the LDF, and the computation of the relevant risk measures. These dynamic approaches are compared with static traditional methodologies in order to show their impact on the capital charges, using several data sets. The construction of the related LDFs and the computation of the capital charges permit complying with the regulation. Besides, capturing simultaneously autocorrelation phenomena and large losses by fitting adequate distributions on the residuals, provide an alternative to the arbitrary selection of the LDA.