Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood

Financial returns exhibit conditional heteroscedasticity, asymmetric responses of their volatility to negative and positive returns (leverage effects) and fat tails. The αα-stable distribution is a natural candidate for capturing the tail-thickness of the conditional distribution of financial returns, while the GARCH-type models are very popular in depicting the conditional heteroscedasticity and leverage effects. However, practical implementation of αα-stable distribution in finance applications has been limited by its estimation difficulties. The performance of the indirect inference approach using GARCH models with Student’s tt distributed errors as auxiliary models is compared to the maximum likelihood approach for estimating GARCH-type models with symmetric αα-stable innovations. It is shown that the expected efficiency gains of the maximum likelihood approach come at high computational costs compared to the indirect inference method.