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Analytic solutions for optimal statistical arbitrage trading

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  • Bertram, William K.

Abstract

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.

Suggested Citation

  • Bertram, William K., 2010. "Analytic solutions for optimal statistical arbitrage trading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2234-2243.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:11:p:2234-2243
    DOI: 10.1016/j.physa.2010.01.045
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    References listed on IDEAS

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    1. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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