Maximum Likelihood Estimation for Conditionally Heteroscedastic Models   when the Innovation Process is in the Domain of Attraction of a Stable Law
  We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only suppose that the innovation process converges in distribution toward a stable process. Using a pseudo maximum likelihood estimator with a stable density, we also obtain the strong consistency and the asymptotic normality of the estimator. This framework seems relevant for financial data exhibiting heavy tails. We apply this method to several financial index and compute stable Value-at-Risk. 
Guillaume Lepage
math.ST stat.TH