Pairs trading with stock borrowing fee
在均值-方差框架下研究带股票借券费用的配对交易策略，通过动态规划和BSDE方法推导出半封闭形式的均衡策略，并用深度学习进行数值求解。
Pairs trading is a strategy that involves simultaneously longing one asset and shorting another related asset, aiming to profit from the price difference between them. In this paper, we discuss a pairs trading problem with stock borrowing fee under a mean-variance (MV) framework. We assume that the difference in the logarithm of two stock prices follows an OU process and focus on the trading strategy that always shorts one stock and longs the other in equal dollar amount. When borrowing stocks for short selling, an interest fee is incurred. By combining dynamic programming and BSDE methods, we establish the existence of solutions to the BSDE and, based on this result, derive a semi-closed-form equilibrium strategy that can be decomposed into three parts: the first part reflects myopic demand, which is expressed as a linear function of the price spread. The second part, characterized by the solution of a BSDE, represents hedging demand. The third part arises from the stock borrowing fee. We also consider the impact of trading constraints on the equilibrium strategy. Finally, we adopt a deep learning-based approach to numerically solve the problem and present simulation results to show the performance of the equilibrium strategy.