Kernel Estimation of Spot Volatility with Microstructure Noise Using Pre-Averaging

TL;DR

This paper introduces a new pre-averaging kernel estimator for ultra high-frequency financial data to accurately estimate spot volatility amidst microstructure noise, supported by theoretical proofs and empirical validation.

Contribution

It proposes a novel pre-averaging kernel estimator with proven optimal convergence rates and minimal asymptotic variance, improving volatility estimation under microstructure noise.

Findings

The estimator achieves optimal convergence rates.

Asymptotic variance is minimized with exponential kernels.

Monte Carlo experiments show superior performance.

Abstract

We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new pre-averaging/kernel estimator for spot volatility to handle the microstructure noise of ultra high-frequency observations. We prove a Central Limit Theorem for the estimation error with an optimal rate and study the optimal selection of the bandwidth and kernel functions. We show that the pre-averaging/kernel estimator's asymptotic variance is minimal for exponential kernels, hence, justifying the need of working with kernels of unbounded support as proposed in this work. We also develop a feasible implementation of the proposed estimators with optimal bandwidth. Monte Carlo experiments confirm the superior performance of the devised method.