Evolutionary Multi-Objective Optimization for ultivariate Pair Trading in Tehran Stock Exchange: The Cointegration Approach

Pair trading strategy is one of the oldest and most common statistical arbitrage strategies. Pair formation is an important step in pair trading that examined manually and this method fails in the multivariate mode and does not consider conflicting goals in the problem structure. The main problem in this study is to present a method that creates multivariate pair combinations with multiple contradictory goals and focusing on the integration approach. Therefore, a combination of stocks optimized for two opposite objectives risk (mean-reversion) and return (spread variance) to form a set of profitable multivariate pair trading opportunities. The statistical population is companies listed on the Tehran Stock Exchange. The statistical sample limited by the need for high-frequency transactions from the top 50 companies. The problem developed in the form of a mixed integer-programming model (MIP), and due to non-convex constraints and exponential space, a multi-objective genetic algorithm used to obtain pair combinations. To achieve multiple goals, an advanced type of genetic algorithm; The Chaotic Non-dominated Sorting Genetic Algorithm (CNSGA-II) was used. The Chaos theory used to create the initial population of the genetic algorithm in order to obtain appropriate and high-precision solutions. Research has shown that the use of chaos theory can increase the degree of convergence in evolutionary algorithms. The results of the experiments of this study show that multi-objective pair trading strategies focusing on the integration approach have a significant advantage over the traditional single-objective model.