Abstract
Continuous-time pairs-trading rules are often developed based on the diffusion limit of first-order autoregressive cointegration models. Empirical identification of cointegration effects is generally made according to discrete-time error correction representation of general vector autoregressive moving average (VARMA($p,q$)) processes. We show that the diffusion limit of a VARMA($p,q$) process appears as a stochastic delayed differential equation. Motivated by this, we investigate the dynamic portfolio problem under a class of path-dependent models embracing path-dependent cointegration models in continuous time as special cases. Under certain reasonable conditions, we prove the existence of the optimal strategy and show that it is related to a system of differential equations. The proof is developed by means of functional It\^{o}'s calculus. When the process satisfies cointegration conditions, our results lead to the optimal dynamic pairs-trading rule. By contrasting our strategy with a pairs-trading strategy that ignores the path-dependent effect (or serial dependency), we numerically demonstrate the superiority of our strategy.
Published Version
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