University of ULM Germany

Despite the ability of the stochastic volatility models along with their multivariate and multi-factor extension to describe the dynamics of the asset returns, these
models are very difficult to calibrate to market information. The recent financial crises, however, highlight that we can not use simplified models to describe the fincancial returns. Therefore, our statistical methodologies have to be improved. We propose a non parametricmethodology based on the use of the Fourier transform and the high frequency data which allows to estimate the diffusion and the leverage components of a general stochastic volatility model driven by continuous Brownian semimartingales. Our estimation procedure is based only on a pre-estimation of the Fourier coefficients of the volatility process and on the use of the Bohr convolution product as in Malliavin and Mancino 2009. This approach constitutes a novelty in comparison with the non-parametric methodologies proposed in the literature generally based on a pre-estimation of the spot volatility and in virtue of its definition it can be directly applied in the case of irregular tradingobservations of the price path an microstructure noise contaminations.