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A Study of Value-at-Risk Based on M-Estimators of the Conditional Heteroscedastic Models


Kanchan Mukherjee, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK. E-mail:


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. Copyright © 2011 John Wiley & Sons, Ltd.