Pairs trading under delayed cointegration

Continuous-time pairs trading rules are often developed based on the diffusion limit of the first-order vector autoregressive (VAR(1)) cointegration models. Empirical identification of cointegration effects is generally made according to discrete-time error correction representation of vector autoregressive (VAR(p)) processes, allowing for delayed adjustment of the price deviation. Motivated by this, we investigate the continuous-time dynamic pairs trading problem under a class of path-dependent models. Under certain regular conditions, we prove the existence of the optimal strategy and show that it is related to a system of Riccati partial differential equations. The proof is developed by the means of functional Itô's calculus. We conduct a numerical study to analyze the sensitivities of the pairs trading strategy with respect to the initial market conditions and the memory length.