Fourier inference for stochastic volatility models with heavy-tailed innovations

Abstract

We consider estimation of stochastic volatility models which are driven by a heavy-tailed innovation distribution. Exploiting the simple structure of the characteristic function of suitably transformed observations we propose an estimator which minimizes a weighted $L^2$-type distance between the theoretical characteristic function of these observations and an empirical counterpart. A related goodness-of-fit test is also proposed. Monte-Carlo results are presented. The procedures are also applied to real data from the financial markets.