The effect of fat tails on rules for optimal pairs trading : performance implications of regime switching with poisson events

This study examines the impact that fat-tailed distributions of the spread residuals have on the optimal orders for pairs trading of stocks and cryptocurrencies. Using daily data from selected pairs, the spread dynamics has been modeled through a mean-reverting Ornstein-Uhlenbeck process and investigates how deviations from normality affect strategy design and profitability. Specifically, we compared four fat-tailed distributions - Lévy stable, generalized hyperbolic, Johnson's SU, and non-centered Student's t - and showed how they modify optimal entry and exit thresholds, and performance metrics. The main findings reveal that the proposed pairs trading strategy correctly captures some key stylized facts of residual spreads such as large jumps, skewness, and excess Kurtosis. Interestingly, we considered regime-switching behaviors to account for structural changes in market dynamics, providing empirical evidence that optimal trading rules are regime-dependent and significantly influenced by the residual distribution's tail behavior. Unlike conventional approaches, we optimized the entry signal and link heavy tails not only to volatility clustering but also to the nonlinearity in switching regimes. These findings suggest the need to account for distributional properties and dynamic regimes when designing robust pairs trading strategies, providing a more realistic and effective framework of these strategies in highly volatile and non-normal markets.