Indirect estimation of alpha-stable stochastic volatility models

The alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its many useful properties, including a central limit theorem, are especially appreciated in the financial field. However, estimation difficulties have up to now hindered its diffusion among practitioners. In this paper we propose an indirect estimation approach to stochastic volatility models with alpha-stable innovations that exploits, as auxiliary model, a GARCH(1,1) with t-distributed innovations. We consider both cases of heavytailed noise in the returns or in the volatility. The approach is illustrated by means of a detailed simulation study and an application to currency crises.