Indirect estimation of α-stable stochastic volatility models

The α-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 α-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. ∗Corresponding author: Dipartimento di Statistica “G. Parenti”, Università di Firenze. Viale G.B. Morgagni 59, I-50134 Firenze (ITALY) Telephone +39-055-4237217, FAX +39-055-4223560, email [email protected]. A preliminary version of this paper was presented at the Fall 2005 Bundesbank conference in honor of the 80th birthday of Prof. Benoı̂t 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.