Computation of volatility in stochastic volatility models with high frequency data

We consider general stochastic volatility models driven by continuous Brownian semi- martingales, we show that the volatility of the variance and the leverage (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.