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Robust statistical arbitrage strategies

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  • Eva Lütkebohmert
  • Julian Sester

Abstract

We investigate statistical arbitrage strategies when there is ambiguity about the underlying time-discrete financial model. Pricing measures are assumed to be martingale measures calibrated to prices of liquidly traded options, whereas the set of admissible physical measures is not necessarily implied from market data. Our investigations rely on the mathematical characterization of statistical arbitrage, which was originally introduced by Bondarenko [Statistical arbitrage and securities prices. Rev. Financ. Stud., 2003, 16, 875–919]. In contrast to pure arbitrage strategies, statistical arbitrage strategies are not entirely risk-free, but the notion allows one to identify strategies which are profitable on average, given the outcome of a specific σ-algebra. Besides a characterization of robust statistical arbitrage, we also provide a super-/sub-replication theorem for the construction of statistical arbitrage strategies for path-dependent options. In particular, we show that the range of statistical arbitrage-free prices is, in general, much tighter than the range of arbitrage-free prices.

Suggested Citation

  • Eva Lütkebohmert & Julian Sester, 2021. "Robust statistical arbitrage strategies," Quantitative Finance, Taylor & Francis Journals, vol. 21(3), pages 379-402, March.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:3:p:379-402
    DOI: 10.1080/14697688.2020.1824077
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    Cited by:

    1. Derek Singh & Shuzhong Zhang, 2021. "Robust Arbitrage Conditions for Financial Markets," SN Operations Research Forum, Springer, vol. 2(3), pages 1-52, September.
    2. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.

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