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December 2013 Analysis of the discrete Ornstein-Uhlenbeck process caused by the tick size effect
Daniel Wei-Chung Miao
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J. Appl. Probab. 50(4): 1102-1116 (December 2013). DOI: 10.1239/jap/1389370102

Abstract

This paper provides an analysis on a discrete version of the Ornstein-Uhlenbeck (OU) process which reflects the small discrete movements caused by the tick size effect. This discrete OU process is derived from matching the first two moments to those of the standard OU process in an infinitesimal sense. We discuss the distributional convergence from the discrete to the continuous processes, and show that the convergence speed is in the second order of the step (tick) size. We also provide some analytical results for the proposed discrete OU process itself, including the closed-form formula of the moment generating function and a full characterisation of the steady state distribution. These results enable us to examine the convergence order explicitly.

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Daniel Wei-Chung Miao. "Analysis of the discrete Ornstein-Uhlenbeck process caused by the tick size effect." J. Appl. Probab. 50 (4) 1102 - 1116, December 2013. https://doi.org/10.1239/jap/1389370102

Information

Published: December 2013
First available in Project Euclid: 10 January 2014

zbMATH: 1296.60228
MathSciNet: MR3161376
Digital Object Identifier: 10.1239/jap/1389370102

Subjects:
Primary: 60G20 , 60J27
Secondary: 60G15 , 60J75

Keywords: convergence order , Discrete Ornstein-Uhlenbeck process , moment generating function , moment matching , steady state , tick size

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 4 • December 2013
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