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用止损与杠杆优化统计套利策略

文章 arXiv papers · 作者: Roberto Baviera et al.
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总结

本文在均值回归交易框架中加入止损规则和杠杆。研究将证券价格建模为奥恩斯坦–乌伦贝克过程，并通过自融资投资组合评估重复交易，同时计入比例交易成本。针对每个选定的止损水平，研究推导出最优杠杆及市场进出场阈值。

分析将策略收益与触及这些阈值的概率、预期首次到达时间，以及过程离开价格区间的预期时间联系起来。研究基于奥恩斯坦–乌伦贝克假设给出离场时间的解析表达式，并将长期收益表示为止损水平的函数。文中举例分析一组取暖油与瓦斯油期货价差，使用一年样本的半小时价格数据。研究发现基于模型，并且仅适用于该特定示例；本文未提供更广泛的证据，无法证明该策略在其他市场中或计入模型所涵盖的交易成本之外的实施摩擦后仍能盈利。

核心观点

  • 该框架为均值回归统计套利策略加入止损水平和杠杆。
  • 最优杠杆以及进出场阈值取决于选定的止损水平。
  • 收益分析使用触及阈值的概率，以及预期首次到达和首次离开时间。
  • 奥恩斯坦–乌伦贝克模型可用于解析处理区间离场时间和长期收益。
  • 研究以取暖油与瓦斯油期货价差为例，使用一年样本的半小时数据说明该方法。

标签

期货大宗商品均值回归配对交易套利风险管理
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# Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market


# Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market









In this paper we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and leverage in an optimal trading strategy. We focus on repeated strategies using a self-financing portfolio. For every given stop-loss level we derive analytically the optimal investment strategy consisting of optimal leverage and market entry/exit levels. First we show that the optimal strategy a' la Bertram depends on the probabilities to reach entry/exit levels, on expected First-Passage-Times and on expected First-Exit-Times from an interval. Then, when the underlying log-price follows an Ornstein-Uhlenbeck process, we deduce analytical expressions for expected First-Exit-Times and we derive the long-run return of the strategy as an elementary function of the stop-loss. Following industry practice of pairs trading we consider an example of pair in the energy futures' market, reporting in detail the analysis for a spread on Heating-Oil and Gas-Oil futures in one year sample of half-an-hour market prices.

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。