Indirect estimation of α-stable stochastic volatility models Marco J. Lombardi Universit` a di Pisa Giorgio Calzolari * Universit` a di Firenze May 23, 2007 Abstract 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. * Corresponding author: Dipartimento di Statistica “G. Parenti”, Universit` a di Firenze. Viale G.B. Morgagni 59, I-50134 Firenze (ITALY) Telephone +39-055-4237217, FAX +39-055-4223560, email calzolar@ds.unifi.it. A preliminary version of this paper was presented at the Fall 2005 Bun- desbank conference in honor of the 80th birthday of Prof. Benoˆ ıt Mandelbrot. We thank Uta Kretschmer for her useful and insightful discussion and Casper de Vries and Mico Loretan for their suggestions and comments. The views expressed are solely those of the authors and do not necessarily reflect the opinion of the European Central Bank. 1