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...

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...

We develop the classical asset pricing analysis assuming that the representative agent is characterized by endogenous aspirations. The agent's aspirations at time t are given by a linear combination of the standard of living (habit) at time t (the “forward” part) and of the conditional...

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...

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the...

We present a methodology based on Fourier series analysis to compute time series volatility when the data are observations of a semimartingale. The procedure is not based on the Wiener theorem for the quadratic variation, but on the computation of the Fourier coefficients of the process and...

In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous It\^o semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot.