We study the forecasting performance of the Fourier volatility estimator in the presence of microstructure noise. Analytical comparison and simulation studies indicate that the Fourier estimator significantly outperforms realized volatility-type estimators, particularly for high-frequency data...

We consider general stochastic volatility models driven by continuous Brownian semimartinagales, we show that asset price volatility as well as volatility of the volatility ca be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying...

In general, a comparison Lemma for the solutions of Forward-Backward Stochastic Differential Equations (FBSDE) does not hold. Here we prove one for the backward component at the initial time, relying on certain monotonicity conditions on the coefficients of both components. Such a result is...