Indirect estimation of α-stable stochastic volatility models

The α-stable family of distributions constitutes a generalization of the Gaus-sian distribution, allowing for asymmetry and thicker tails. Its many useful prop-erties, 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 stochas-tic volatility models with α-stable innovations that exploits, as auxiliary model, a GARCH(1,1) with t-distributed innovations. We consider both cases of heavy-tailed 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