Ait-Sahalia, Y. and Jacod, J. (2009) Testing for Jumps in a Discretely Observed Process. Annals of Statistics, 37, 184-222.
ABSTRACT: This paper proposes a simple two-step nonparametric procedure to estimate the intraday jump tail and measure the jump tail risk in asset price with noisy high frequency data. We first propose the pre-averaging threshold approach to estimate the intraday jumps occurred, and then use the peaks-over-threshold (POT) method and generalized Pareto distribution (GPD) to model the intraday jump tail and further measure the jump tail risk. Finally, an empirical example further demonstrates the power of the proposed method to measure the jump tail risk under the effect of microstructure noise.