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交易约束下的最优配对交易退出规则

文章 arXiv papers · 作者: Ruyi Liu et al.
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总结

本文研究何时平掉股票配对交易头寸，即一只股票做多、另一只做空。文中将退出决策表述为受交易约束的最优卖出与回购问题。模型假设两只股票价格遵循二维几何布朗运动，而是否允许交易由一个两状态马尔可夫链决定。

所提最优策略由一个阈值曲线刻画，该曲线通过求解相应的哈密尔顿—雅可比—贝尔曼拟变分不等式得出。论文报告了闭式解，并给出验证定理以支持所称的最优性。数值实验展示了所得策略和价值函数。这些结论取决于所设定的价格动态和交易许可过程；摘要没有基于市场数据进行实证评估，也未考虑交易成本，且没有证明该规则在实盘交易中优于其他退出方法。

核心观点

  • 问题是在交易可行性受限时，选择何时平掉一对多空股票头寸。
  • 模型以二维几何布朗运动表示两只股票的价格。
  • 两状态马尔可夫链决定当前是否允许交易。
  • 通过求解 HJB 拟变分不等式，得到由阈值曲线描述的最优退出策略。
  • 论文报告了闭式解、验证定理和数值示例。

标签

股票配对交易均值回归统计学
全文
# Pairs Trading: An Optimal Selling Rule with Constraints


# Pairs Trading: An Optimal Selling Rule with Constraints









The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the optimal time to sell the long position and repurchase the short position in order to close the pairs position. The paper presents an optimal pairs-trading selling rule with trading constraints. In particular, the underlying stock prices evolve according to a two dimensional geometric Brownian motion and the trading permission process is given in terms of a two-state {trading allowed, trading not allowed} Markov chain. It is shown that the optimal policy can be determined by a threshold curve which is obtained by solving the associated HJB equations (quasi-variational inequalities). A closed form solution is obtained. A verification theorem is provided. Numerical experiments are also reported to demonstrate the optimal policies and value functions.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。