Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 389, Issue 11, Pages 2234-2243Publisher
ELSEVIER
DOI: 10.1016/j.physa.2010.01.045
Keywords
Econophysics; Stochastic processes; First-passage time
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In this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an Ornstein-Uhlenbeck process. By framing the problem in terms of the first-passage time of the process, we derive expressions for the mean and variance of the trade length and the return. We examine the problem of choosing an optimal strategy under two different objective functions: the expected return, and the Sharpe ratio. An exact analytic solution is obtained for the case of maximising the expected return. (C) 2010 Elsevier B.V. All rights reserved.
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