Robust Statistical Arbitrage Strategies

28 Pages Posted: 16 Aug 2019

See all articles by Eva Lütkebohmert

Eva Lütkebohmert

University of Freiburg, Institute for Economic Research

Julian Sester

University of Freiburg

Date Written: August 13, 2019


We investigate statistical arbitrage strategies when there is ambiguity about the underlying 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: or

Eva Lütkebohmert

University of Freiburg, Institute for Economic Research ( email )

Platz der Alten Synagoge 1
Freiburg, D-79098

Julian Sester (Contact Author)

University of Freiburg

Freiburg, D-79085

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics