Pairs trading with topological data analysis

Abstract

In this paper, we propose a pairs trading strategy using the theory of topological data analysis (TDA). The proposed strategy is model-free. We propose a TDA-based distance to measure dependence between a pair of stochastic processes. We derive an upper bound of this distance in terms of a function of the canonical correlation of the processes, which allows for interpretability of this distance. We also study Karhunen–Loève expansions of certain processes to qualitatively explore their shape properties. We check the performance of the strategy on simulated data from correlated geometric Brownian motion, correlated Ornstein–Uhlenbeck process and DCC-GARCH. We also examine the profitability of the proposed strategy on high-frequency data from the National Stock Exchange of India in 2018. We compare the method to a Euclidean distance-based method for pairs trading. We propose a pairs trading strategy evaluation framework using a Bayesian model for comparing gains from these two strategies. We find that the proposed approach based on TDA is more profitable and trades more frequently than the Euclidean distance-based strategy.