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几何布朗运动价格下的阈值往返配对交易

文章 arXiv papers · 作者: Emily Crawford Das et al.
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总结

本文构建一种双股票配对交易策略，假设两只股票的价格遵循一般几何布朗运动，而不假设其价差均值回归。交易者比较两只股票的相对强弱，做空较强的股票并买入较弱的股票建立仓位，随后在相对表现反转时尝试平仓。每笔交易均收取固定佣金，目标是最大化开仓和平仓交易的整体收益。

分析通过哈密顿–雅可比–贝尔曼方程推导的阈值曲线刻画最优决策。研究考虑两种初始仓位设定：初始为多头或空仓，以及初始为多头、空仓或空头。所提供的描述介绍了模型和求解方法，但没有给出数值结果、数据测试或参数估计细节。因此，结论仅针对所述随机模型；实际表现取决于价格和成本假设与真实市场的契合程度。

核心观点

  • 模型允许每只股票价格遵循几何布朗运动，无需假设价差均值回归。
  • 交易将较强股票的空头仓位与较弱股票的多头仓位配对。
  • 往返交易中的每笔交易均收取固定佣金。
  • 最优开仓和平仓策略由 HJB 方程推导出的阈值曲线表示。
  • 论文分析了初始仓位为多头或空仓，以及多头、空仓或空头两种选择。

标签

股票配对交易均值回归风险管理
全文
# Optimal Strategies for Round-Trip Pairs Trading Under Geometric Brownian Motions


# Optimal Strategies for Round-Trip Pairs Trading Under Geometric Brownian Motions









This paper is concerned with an optimal strategy for simultaneously trading a pair of stocks. The idea of pairs trading is to monitor their price movements and compare their relative strength over time. A pairs trade is triggered by the divergence of their prices and consists of a pair of positions to short the strong stock and to long the weak one. Such a strategy bets on the reversal of their price strengths. A round-trip trading strategy refers to opening and closing such a pair of security positions. Typical pairs-trading models usually assume a difference of the stock prices satisfies a mean-reversion equation. However, we consider the optimal pairs-trading problem by allowing the stock prices to follow general geometric Brownian motions. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. Initially, we allow the initial pairs position to be either long or flat. We then consider the problem when the initial pairs position may be long, flat, or short. In each case, the optimal policy is characterized by threshold curves obtained by solving the associated HJB equations.

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。