论文标题
在存在微观结构噪声的情况下，傅里叶斑点波动率估计器的渐近正态性
Asymptotic Normality for the Fourier spot volatility estimator in the presence of microstructure noise
论文作者
论文摘要
本文的主要贡献证明，如果价格过程受到微观结构噪声污染，则[Malliavin和Mancino，2002]中引入的傅立叶斑点波动率估计器是一致的，渐近效率是渐近的。具体而言，在存在添加微结构噪声的情况下，我们证明了一个中心限制定理，最佳收敛速率$ n^{1/8} $。结果是无需操纵原始数据或偏置校正的。此外，我们通过在[Mancino and Recchioni，2015]中呈现的傅立叶斑点波动估计器的渐近理论，该理论以最佳收敛速率$ n^{1/4} $得出中心限制定理，以最初呈现[Mancino and Recchioni，2015]。最后，我们提出了一种新型的可行自适应方法，以最佳选择具有嘈杂的高频数据的傅立叶点波动率估计器所涉及的参数，并在数值和经验上为其准确性提供了支持。
The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and Mancino, 2002] is consistent and asymptotically efficient if the price process is contaminated by microstructure noise. Specifically, in the presence of additive microstructure noise we prove a Central Limit Theorem with the optimal rate of convergence $n^{1/8}$. The result is obtained without the need for any manipulation of the original data or bias correction. Moreover, we complete the asymptotic theory for the Fourier spot volatility estimator in the absence of noise, originally presented in [Mancino and Recchioni, 2015], by deriving a Central Limit Theorem with the optimal convergence rate $n^{1/4}$. Finally, we propose a novel feasible adaptive method for the optimal selection of the parameters involved in the implementation of the Fourier spot volatility estimator with noisy high-frequency data and provide support to its accuracy both numerically and empirically.
