Rate Efficient Asymptotic Normality for the Fourier Estimator of the Leverage Process

We prove a Central Limit Theorem for two estimators of the le verage pro cess based on the Fourier method of Malliavin and Mancino [26], showing that they reach the optimal rate 1/4 and a smaller variance compared to different estimators based on a pre-estimation of the instantaneous volatility. The obtained limiting distributions of the estimators are supported by simulation results. Further, we exploit the availability of efficient leverage estimates to show, using S&P500 prices, that adding an extra term which accounts for the leverage effect to the Heterogeneous AutoRegressive volatility model by Corsi [13] increases the explanatory power of the latter.