Outliers in GARCH models and the estimation of risk measures

In this paper we focus on the impact of additive level outliers on the calculation of risk measures such as minimum capital risk requirements and four possible alternatives of reducing these measures’ estimation biases. The first and second alternatives are based on wavelets while the third is based on the traditional proposals in the literature and the three are based on the detection and correction of outliers before the estimation of these risk measures. On the other hand, the fourth alternative fits a t-distributed GARCH(1,1) directly to the “contaminated” data. The first results based on Monte Carlo experiments reveal that the presence of these observations can bias severely the minimum capital risk requirement estimates calculated using the GARCH(1,1) model. This finding is quite relevant since it can generate losses for those financial institutions that calculate GARCH model based minimum capital risk requirements. The message driven from the second results, both empirical and simulations, is: outlier detection and correction generates more accurate minimum capital risk requirements than the fourth alternative. Moreover, the detection procedure based on wavelets with hard-thresholding correction gathers a very good performance in attenuating the effects of outliers and generating accurate minimum capital risk requirements out-of-sample, even in pretty volatile periods. JEL classification: Minimum Capital Risk Requirements, Outliers, Wavelets