NON‐PARAMETRIC ESTIMATION OF HIGH‐FREQUENCY SPOT VOLATILITY FOR BROWNIAN SEMIMARTINGALE WITH JUMPS

Abstract

The availability of high‐frequency financial data has led to substantial improvements in our understanding of financial volatility. Most existing literature focuses on estimating the integrated volatility over a fixed period. This article proposes a non‐parametric threshold kernel method to estimate the time‐dependent spot volatility and jumps when the underlying price process is governed by Brownian semimartingale with finite activity jumps. The threshold kernel estimator combines the threshold estimation for integrated volatility and the kernel filtering approach for spot volatility when the price process is driven only by diffusions without jumps. The estimator proposed is consistent and asymptotically normal and has the same rate of convergence as the estimator studied by Kristensen (2010) in a setting without jumps. The Monte Carlo simulation study shows that the proposed estimator exhibits excellent performance over a wide range of jump sizes and for different sampling frequencies. An empirical example is given to illustrate the potential applications of the proposed method.