带Poisson跳和杠杆效应的资产价格时点波动非参数估计

Nonparametric Estimation for Spot Volatility of Asset Price with Leverage Effects and Poisson Jumps

本文采用时间序列核平滑技术和跳消除方法,对带Poisson跳和杠杆效应的资产格时点波动(Spot Volatility)进行估计。采用随机阵列极限理论,证明了估计量存在杠杆效应时的一致性和渐进正态性,采用门限方法消除资产价格中Poisson跳对时点波动估计的影响,对现有文献中资产价格连续并且无杠杆效应假设下的时点波动估计量进行了实质性改进和推广。本文分析估计量的有限样本偏差并给出了纠偏的方法。蒙特卡洛模拟表明,本文给出的估计量明显优于文献中现有估计量。

Using kernel-smoothing technique and threshold jump-annihilating method, This paper proposes a new spot volatility estimator of asset prices with le- verage effects and presence of poisson jumps. The consistency and asymptotic nor- mality is established. The article also analyzes the finite-sample bias of the estima- tor and gives a bias-correction version. An extensive Monte Carlo simulation shows that the estimator in the paper outperforms the other in literature significantly.