Generalized Statistical Arbitrage Across Defined Market States

Summary

The paper broadens statistical arbitrage by defining gains in relation to specified market states, represented by an information system such as a sigma-algebra. Its framework includes classical arbitrage as a special case and also encompasses the statistical arbitrage concept attributed to Bondarenko. The authors further introduce generalized profitable strategies, which can include static and semi-static positions.

The paper characterizes these generalized notions of statistical no-arbitrage and constructs strategies for different choices of information system. Examples include embedded binomial, follow-the-trend, and partition-based strategies. Their behavior is compared using simulated data, and the authors also report favorable performance on market data. These results suggest that a standard no-arbitrage condition can coexist with strategies that have positive average gains under selected scenarios. The abstract does not give implementation details, transaction-cost estimates, or enough information to assess how robust the reported market performance is in live trading.

Key ideas

• The framework defines average gains over specified market states rather than requiring gains almost surely.
• Classical arbitrage and Bondarenko-style statistical arbitrage appear as special cases within the broader framework.
• Generalized profitable strategies can include static and semi-static positions.
• The paper studies embedded binomial, trend-following, and partition-based strategies in simulations and market data.
• Standard no-arbitrage conditions may still allow positive average gains for a defined set of scenarios.

Tags

# Generalized statistical arbitrage concepts and related gain strategies


# Generalized statistical arbitrage concepts and related gain strategies









Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via an information system given by a $σ$-algebra and so this notion contains classical arbitrage as a special case. It also covers the notion of statistical arbitrage introduced in Bondarenko (2003). Relaxing these notions further we introduce generalized profitable strategies which include also static or semi-static strategies. Under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios. In the first part of the paper we characterize these generalized statistical no-arbitrage notions. In the second part of the paper we construct several profitable generalized strategies with respect to various choices of the information system. In particular, we consider several forms of embedded binomial strategies and follow-the-trend strategies as well as partition-type strategies. We study and compare their behaviour on simulated data. Additionally, we find good performance on market data of these simple strategies which makes them profitable candidates for real applications.

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