Detecting jumps in high-frequency prices under stochastic volatility:a data-driven approach

Tsai, Ping-Chen and Shackleton, Mark (2016) Detecting jumps in high-frequency prices under stochastic volatility:a data-driven approach. In: Handbook of high-frequency trading and modeling in finance. John Wiley, Chichester, pp. 137-165. ISBN 9781118443989

Abstract

Detecting jumps in asset prices over a daily interval consists of testing for the significance of the difference between quadratic variation and integrated variance. Detecting jumps in high-frequency prices requires the additional tasks of estimating spot volatility and controlling for over-rejection due to multiple comparisons. We generalize two intraday tests commonly used in the literature and identify the test statistic that has the highest power at a given test level. The daily maximums of such test statistics admit an asymptotic generalized extreme value (GEV) distribution with a strictly positive shape parameter, as opposed to the limiting Gumbel distribution with a shape parameter zero for i.i.d. Gaussian maximums. The shape parameter of GEV distribution can thus be seen as a measure of bias correction for the test under stochastic volatility. We calibrate the shape parameter with a credible volatility model estimated from our data, which are Spyder (SPY) returns during January, 2002 and April, 2010. Empirical results are broadly consistent with those from simulation.