Robust Statistical Arbitrage Strategies

34 Pages Posted: 16 Aug 2019 Last revised: 27 Jul 2020

See all articles by Eva Lütkebohmert

Eva Lütkebohmert

University of Freiburg, Institute for Economic Research

Julian Sester

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences; University of Freiburg

Date Written: August 13, 2019

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 in 2003. In contrast to pure arbitrage strategies, statistical arbitrage strategies are not entirely risk-free, but the notion allows to identify strategies which are profitable on average, given the outcome of a specific sigma-algebra. Besides a characterization of robust statistical arbitrage, we also provide a super-/sub-replication theorem for the construction of statistical arbitrage strategies based on 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.

Keywords: Statistical Arbitrage, Robust Valuation, Trading Strategies, Super-Replication Duality

JEL Classification: G11, G13, G24

Suggested Citation

Lütkebohmert, Eva and Sester, Julian, Robust Statistical Arbitrage Strategies (August 13, 2019). Available at SSRN: https://ssrn.com/abstract=3436788 or http://dx.doi.org/10.2139/ssrn.3436788

Eva Lütkebohmert

University of Freiburg, Institute for Economic Research ( email )

Platz der Alten Synagoge 1
Freiburg, D-79098
Germany

Julian Sester (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

University of Freiburg

Freiburg, D-79085
Germany

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