Kernel filtering of spot volatility in presence of Lévy jumps and market microstructure noise

This paper considers the problem of estimating spot volatility in the simultaneous presence of Lévy jumps and market microstructure noise. We propose to use the pre-averaging approach and the threshold kernel-based method to construct a spot volatility estimator, which is robust to both microstructure noise and jumps of either finite or infinite activity. The estimator is consistent and asymptotically normal, with a fast convergence rate. Our estimator is general enough to include many existing kernel-based estimators as special cases. When the kernel bandwidth is fixed, our estimator leads to widely used estimators of integrated volatility. Monte Carlo simulations show that our estimator works very well.