Analytic Solutions for Optimal Statistical Arbitrage Trading
William Karel Bertram
ITG Australia Limited
November 12, 2009
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.
Number of Pages in PDF File: 16
Keywords: Econophysics, Stochastic Processes, First Passage Time
JEL Classification: C00working papers series
Date posted: November 14, 2009
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