A General Framework for Pairs Trading with a Control-Theoretic Point of View

TL;DR

This paper introduces a control-theoretic framework for pairs trading that requires fewer assumptions, allowing dynamic adjustment of investment levels based on a flexible spread function, and demonstrates its effectiveness through historical data tests.

Contribution

It presents a novel, less restrictive, control-inspired pairs trading algorithm that adapts to arbitrary spread functions and guarantees positive expected growth under mean-reversion conditions.

Findings

Algorithm achieves robust growth in historical data tests.

It avoids large drawdowns during trading.

The method requires fewer assumptions than traditional models.

Abstract

Pairs trading is a market-neutral strategy that exploits historical correlation between stocks to achieve statistical arbitrage. Existing pairs-trading algorithms in the literature require rather restrictive assumptions on the underlying stochastic stock-price processes and the so-called spread function. In contrast to existing literature, we consider an algorithm for pairs trading which requires less restrictive assumptions than heretofore considered. Since our point of view is control-theoretic in nature, the analysis and results are straightforward to follow by a non-expert in finance. To this end, we describe a general pairs-trading algorithm which allows the user to define a rather arbitrary spread function which is used in a feedback context to modify the investment levels dynamically over time. When this function, in combination with the price process, satisfies a certain mean-reversion condition, we deem the stocks to be a tradeable pair. For such a case, we prove that our control-inspired trading algorithm results in positive expected growth in account value. Finally, we describe tests of our algorithm on historical trading data by fitting stock price pairs to a popular spread function used in literature. Simulation results from these tests demonstrate robust growth while avoiding huge drawdowns.