We prove a Central Limit Theorem for two estimators of the leverage process 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 Auto-Regressive volatility model by Corsi [13] increases the explanatory power of the latter.

中文翻译：

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杠杆过程傅立叶估计量的速率有效渐近正态性

我们证明了基于 Malliavin 和 Mancino [26] 的傅立叶方法的杠杆过程的两个估计量的中心极限定理，表明与基于预瞬时波动率的估计。获得的估计量的极限分布得到了仿真结果的支持。此外，我们利用有效杠杆估计的可用性来表明，使用标准普尔 500 价格，在 Corsi [13] 的异构自回归波动率模型中添加一个解释杠杆效应的额外项会增加后者的解释力。