A nonparametric approach to estimate volatility and correlation dynamics

We evaluate the performance of a nonparametric method based on Fourier analysis to estimate volatility and correlation as functions of time. Being based on integration rather than on differentiation, the method naturally exploits the inhomogeneous time structure of the high frequency prices and does not required any prior data manipulation. Through Monte Carlo experiments, we show that the method can effectively reconstruct the volatility trajectory of both univariate and bivariate models and it is also able to detect the temporal dependencies between two simulated diffusion processes. On the other hand, our study also emphasizes the sensitivity of the approach to some key quantities related to its numerical implementation.