On optimal thresholds for pairs trading in a one-dimensional diffusion model

Authors

DOI:

https://doi.org/10.21914/anziamj.v63.15437

Keywords:

pairs trading, threshold rule, one-dimensional diffusion, first passage time, long-time averaged profit, asymptotic arbitrage, Pearson Diffusion

Abstract

We study the static maximization of long-term averaged profit, when optimal preset thresholds are determined to describe a pairs trading strategy in a general one-dimensional ergodic diffusion model of a stochastic spread process. An explicit formula for the expected value of a certain first passage time is given, which is used to derive a simple equation for determining the optimal thresholds. Asymptotic arbitrage in the long run of the threshold strategy is observed.

doi:10.1017/S1446181121000298

Author Biographies

Masaaki Fukasawa, Osaka University

Graduate School of Engineering Science, Osaka University, Osaka, Japan.

Hitomi Maeda, Osaka University

Graduate School of Engineering Science, Osaka University, Osaka, Japan.

Jun Sekine, Osaka University

Graduate School of Engineering Science, Osaka University, Osaka, Japan.

Published

2021-10-02

Issue

Vol. 63 (2021)

Section

Special Issue for Financial Mathematics, Probability and Statistics