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

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)

Publication date05/2016
Host publicationHandbook of high-frequency trading and modeling in finance
EditorsIonut Florescu, Maria C. Mariani, H. Eugene Stanley, Frederi G. Viens
Place of PublicationChichester
PublisherJohn Wiley
Number of pages39
ISBN (Print)9781118443989
Original languageEnglish


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.