From Tick Data to Semimartingales

39 Pages Posted: 9 Oct 2017

See all articles by Yacine Ait-Sahalia

Yacine Ait-Sahalia

Princeton University - Department of Economics

Jean M. Jacod

Université Paris VI Pierre et Marie Curie

Date Written: October 6, 2017

Abstract

Tick-by-tick asset price data exhibit a number of empirical regularities, including discreteness, long periods where prices are flat, periods of price moves of alternating plus and minus one tick, periods of rapid successive price moves of the same sign, and others. This paper proposes a framework to examine whether and how these microscopic features of the tick data are compatible with the typical macroscopic continuous-time models, based on Itô semimartingales, that are employed to represent asset prices. We construct in particular tick-by-tick models that deliver by scaling macroscopic semimartingale models with stochastic volatility and jumps.

Keywords: Lévy Process, Semimartingale, Jumps, Scaling, Convergence, Tick by Tick, High Frequency, Continuous Time

JEL Classification: G11

Suggested Citation

Ait-Sahalia, Yacine and Jacod, Jean M., From Tick Data to Semimartingales (October 6, 2017). Available at SSRN: https://ssrn.com/abstract=3049113 or http://dx.doi.org/10.2139/ssrn.3049113

Yacine Ait-Sahalia (Contact Author)

Princeton University - Department of Economics ( email )

Fisher Hall
Princeton, NJ 08544
United States
609-258-4015 (Phone)
609-258-5398 (Fax)

Jean M. Jacod

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

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