Inference procedures for stable-Paretian stochastic volatility models

A discrete stochastic volatility model is considered; the model is driven by two stable-Paretian processes, one for the observations and the other for the scale parameter. Due to the convolution properties of stable-Paretian laws, the unconditional distribution of the observations is also stable-Paretian, and therefore its characteristic function is expressed as a simple exponential-type function incorporating the parameters. Exploiting this feature of the stochastic volatility model considered, methods of estimation are proposed employing the empirical characteristic function. The proposed procedures are applied with simulated data but also with some real data from the financial markets.