An Autocorrelated Loss Distribution Approach: back to the time series
Résumé
The Advanced Measurement Approach requires financial institutions to develop internal models to evaluate their capital charges. 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 current approach suggested by the regulator implemented in the financial institutions assumes the independence of the losses. In this paper, we propose 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 time series processes 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 the choice of the internal models retained by the companies 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-fits tests rejects them -, keeping the LDA modelling corresponds to an arbitrary choice. We suggest in this paper an alternative and robust approach. For instance, for the two data sets we explore in this paper, with the strategies presented in this paper, the independence assumption is released and we are able to capture the autocorrelations inside the losses through the time series modelling. The construction of the related LDF enables the computation of the capital charge and therefore permits complying with the regulation taking into account as the same time the large losses with adequate distributions on the residuals and the correlations between losses with the time series modelling.
L'AMA demande aux institutions de définir leurs modèles internes. Pour les risques opérations, la LDA est la méthode classique. Dans cet article, nous proposons une autre solution prenant en compte l'existence des corrélations entre les pertes. Notre approche est basée sur l'utilisation des processus AR, et les processus Gegenbauer avec différentes distributions pour les résidus. Afin de montrer l'impact du choix des modéles internes retenus par les entreprises sur les exigences de fonds propres.
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