Indirect estimation of αα-stable stochastic volatility models

The αα-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 widespread use among practitioners. The authors introduce an indirect estimation approach to stochastic volatility models with αα-stable innovations that exploits, as auxiliary model, a GARCH(1, 1) with tt-distributed innovations. The approach is illustrated by means of a detailed simulation study and an application to currency crises.