Analysis of the Discrete Ornstein-Uhlenbeck Process Caused by the Tick Size Effect. (30th January 2018)

• Record Type: Journal Article
• Authors: Miao, Daniel Wei-Chung
• Is Part Of: Journal of applied probability. Volume 50:Number 4(2013)
• Page Start: 1102
• Page End: 1116
• Publication Date: 2018-01-30
• Subjects: Discrete Ornstein-Uhlenbeck process, -- moment matching, -- tick size, -- convergence order, -- moment generating function, -- steady state; 60G20, -- 60J27, -- 60G15, -- 60J75; 519.2
• DOI: 10.1239/jap/1389370102
• Languages: English
• ISSNs: 0021-9002

Abstract

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.