In this paper, we investigate the performance of a class of M-estimators for both
symmetric and asymmetric conditional heteroscedastic models in the prediction
of value-at-risk. The class of estimators includes the least absolute deviation
(LAD), Huber’s, Cauchy and B-estimator, as well as the well-known quasi
maximum likelihood estimator (QMLE). We use a wide range of summary
statistics to compare both the in-sample and out-of-sample VaR estimates of
three well-known stock indices. Our empirical study suggests that in general
Cauchy, Huber and B-estimator have better performance in predicting one-step ahead VaR than the commonly used QMLE.