KERNEL ESTIMATION OF SPOT VOLATILITY WITH MICROSTRUCTURE NOISE USING PRE-AVERAGING
研究了使用核估计器估计伊藤半鞅瞬时波动率的问题，提出了新的预平均/核估计器以处理超高频观测中的微观结构噪声，并证明了其最优收敛速度和渐近方差最小化性质。
We revisit the problem of estimating the spot volatility of an Itô semimartingale using a kernel estimator. A central limit theorem (CLT) with an optimal convergence rate is established for a general two-sided kernel. A new pre-averaging/kernel estimator for spot volatility is also introduced to handle the microstructure noise of ultra high-frequency observations. A CLT for the estimation error of the new estimator is obtained, and the optimal selection of the bandwidth and kernel function is subsequently studied. It is shown that the pre-averaging/kernel estimator’s asymptotic variance is minimal for two-sided exponential kernels, hence justifying the need of working with kernels of unbounded support. Feasible implementation of the proposed estimators with optimal bandwidth is developed as well. Monte Carlo experiments confirm the superior performance of the new method.