Documents de Travail du Centre d ’ Economie de la Sorbonne An Autocorrelated Loss Distribution

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 99.9 percentile of the distribution providing the capital charge denotes the worst year in a thousand. The traditional approach approved by the regulator implemented by financial institutions assumes the independence of the losses. This paper proposes a solution to address the issues arising when autocorrelations are detected between the losses. Our approach suggests working with the losses considered as time series. Thus, the losses are aggregated periodically and several models are adjusted on the related time series among AR, ARFI and Gegenbauer processes, and a distribution is fitted on the residuals. Finally a Monte Carlo simulation enables constructing the LDF, and the pertaining risk measures are evaluated. In order to show the impact of internal models retained by financial institutions on the capital charges, the paper draws a parallel between the static traditional approach and an appropriate dynamical modelling. If by implementing the traditional LDA, no particular distribution proves its adequacy to the data as soon as the goodness-of-fit tests reject them keeping the LDA corresponds to an arbitrary choice. This paper suggests an alternative and robust approach. For instance, for the two data sets explored in this paper, with the introduced time series strategies, the independence assumption is released and the autocorrelations embedded within the losses are captured. The construction of the related LDF enables the computation of the capital charges and therefore permits to comply with the regulation taking into account at the same time the large losses with adequate distributions on the residuals, and the correlations between the losses with the time series processes.