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Generalized Statistical Arbitrage Concepts and Related Gain Strategies

Last Updated on 10 February, 2024 by Rejaul Karim

On an exploration of cutting-edge financial strategies, the research paper titled “Generalized Statistical Arbitrage Concepts and Related Gain Strategies” by Christian Rein, Ludger Rüschendorf, and Thorsten Schmidt unveils a novel paradigm in statistical arbitrage.

Departing from conventional wisdom, the paper introduces generalized statistical arbitrage concepts, focusing on trading strategies that yield positive gains on average within specific market scenarios. These scenarios are precisely defined through an information system, offering a nuanced approach that encompasses classical arbitrage and extends to include the notion introduced by Bondarenko (2003). The research further delves into generalized profitable strategies, accommodating static or semi-static approaches.

Remarkably, the study demonstrates the existence of profitable generalized strategies, challenging traditional notions of no-arbitrage. The second part of the paper constructs and analyzes diverse profitable strategies, from embedded binomial and follow-the-trend strategies to partition-type strategies. Through rigorous simulations and real-market data analysis, the paper positions these strategies as promising candidates for practical financial applications.

Abstract Of Paper

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.

Original paper – Download PDF

Here you can download the PDF and original paper of Generalized Statistical Arbitrage Concepts and Related Gain Strategies.

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Author

Christian Rein
University of Freiburg – Institut für Mathematische Stochastik

Ludger Rüschendorf
University of Freiburg

Thorsten Schmidt
University of Freiburg

Conclusion

In conclusion, our exploration into generalized statistical arbitrage unveils a novel perspective on trading strategies—one that transcends classical arbitrage concepts by considering scenarios where positive gains manifest on average within specified market states.

We extend this notion to encompass generalized profitable strategies, accommodating static or semi-static approaches. Remarkably, even under standard no-arbitrage conditions, our framework allows for the existence of generalized gain strategies, adding a layer of flexibility to traditional paradigms.

In the latter part of our study, we practically manifest these concepts through the construction of various profitable generalized strategies, ranging from embedded binomial strategies to follow-the-trend and partition-type strategies. Rigorous simulations and real-market data affirm the efficacy of these strategies, positioning them as promising candidates for practical applications in the dynamic landscape of statistical arbitrage.

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FAQ

– What is the central focus of the research paper “Generalized Statistical Arbitrage Concepts and Related Gain Strategies” and how does it depart from conventional wisdom in statistical arbitrage?

The central focus of the research paper is on introducing generalized statistical arbitrage concepts that deviate from conventional wisdom in statistical arbitrage. Instead of adhering to the notion of gains almost surely, the paper explores trading strategies that yield positive gains on average within specific market scenarios. This departure allows for a more nuanced approach to statistical arbitrage, encompassing classical arbitrage and extending to include broader notions introduced by Bondarenko (2003).

– How does the paper challenge traditional notions of no-arbitrage, and what types of generalized profitable strategies are introduced in the study?

The paper challenges traditional notions of no-arbitrage by demonstrating the existence of generalized gain strategies that yield positive gains on average under specified scenarios, even within standard no-arbitrage conditions. In the second part of the paper, various generalized profitable strategies are introduced. These include embedded binomial strategies, follow-the-trend strategies, and partition-type strategies. The study characterizes, constructs, and analyzes these strategies, showcasing their potential for profitability under different market conditions.

– How does the research validate the practical application of the introduced strategies, and what types of strategies are considered promising candidates for real-world financial applications?

The paper validates the practical application of the introduced strategies through rigorous simulations and analysis of real-market data. The constructed strategies, including embedded binomial strategies, follow-the-trend strategies, and partition-type strategies, exhibit good performance. This positions them as promising candidates for real-world financial applications, highlighting their efficacy and potential in the dynamic landscape of statistical arbitrage.

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