Open Access
December 2020 From tick data to semimartingales
Yacine Aït-Sahalia, Jean Jacod
Ann. Appl. Probab. 30(6): 2740-2768 (December 2020). DOI: 10.1214/20-AAP1571


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.


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Yacine Aït-Sahalia. Jean Jacod. "From tick data to semimartingales." Ann. Appl. Probab. 30 (6) 2740 - 2768, December 2020.


Received: 1 May 2019; Revised: 1 December 2019; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1571

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: continuous time , convergence , high frequency , jumps , Lévy process , scaling , Semimartingale , stochastic volatility

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 6 • December 2020
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