Pairs trading under delayed cointegration
研究了在路径依赖模型下的连续时间配对交易问题，证明了最优策略的存在性及其与Riccati偏微分方程系统的关系，并通过数值分析考察了策略对初始市场条件和记忆长度的敏感性。
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.