Generalized Statistical Arbitrage Concepts and Related Gain Strategies

32 Pages Posted: 24 Jul 2019 Last revised: 28 Jul 2019

See all articles by Christian Rein

Christian Rein

University of Freiburg - Institut für Mathematische Stochastik

Ludger Rüschendorf

University of Freiburg

Thorsten Schmidt

University of Freiburg

Date Written: July 22, 2019

Abstract

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 sigma-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.

Keywords: statistical arbitrage, trading strategy, pairs trading, profitable strategy, good deals

JEL Classification: C02, G11, G24

Suggested Citation

Rein, Christian and Rüschendorf, Ludger and Schmidt, Thorsten, Generalized Statistical Arbitrage Concepts and Related Gain Strategies (July 22, 2019). Available at SSRN: https://ssrn.com/abstract=3423944 or http://dx.doi.org/10.2139/ssrn.3423944

Christian Rein

University of Freiburg - Institut für Mathematische Stochastik

D-79104, Freiburg
Germany

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Thorsten Schmidt (Contact Author)

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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