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带风险约束与参数不确定性的 Bertram 配对交易

文章 arXiv papers · 作者: Vladimír Holý et al.
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总结

本文研究 Bertram 针对一对协整资产提出的最优策略，其价格差遵循 Ornstein–Uhlenbeck 过程。基本目标是最大化单位时间的预期利润。作者进一步在设定中加入单位时间利润波动率约束，以表示策略风险限制，例如监管机构施加的限制。

风险约束可能使优化问题变为非凸问题，但论文表明该问题仍可高效求解。论文还探讨了实际问题：价格过程参数必须根据有限样本估计。分析量化了估计误差对最优策略的影响，以及相较于准确知道参数的交易者，由此造成的损失。本文聚焦于优化和统计不确定性；所提供的说明没有给出数值绩效结果或实证市场验证。

核心观点

  • 该策略将协整资产之间的价差建模为 Ornstein–Uhlenbeck 过程。
  • 基本目标是最大化单位时间的预期利润。
  • 风险约束版本限制利润波动率，可能导致非凸优化问题。
  • 研究表明，该约束问题仍可高效求解。
  • 有限样本下的参数不确定性可能改变最优策略，并使利润低于参数完全已知时的水平。

标签

配对交易均值回归风险管理统计学仓位规模
全文
# Bertram's Pairs Trading Strategy with Bounded Risk


# Bertram's Pairs Trading Strategy with Bounded Risk









Finding Bertram's optimal trading strategy for a pair of cointegrated assets following the Ornstein--Uhlenbeck price difference process can be formulated as an unconstrained convex optimization problem for maximization of expected profit per unit of time. This model is generalized to the form where the riskiness of profit, measured by its per-time-unit volatility, is controlled (e.g. in case of existence of limits on riskiness of trading strategies imposed by regulatory bodies). The resulting optimization problem need not be convex. In spite of this undesirable fact, it is demonstrated that the problem is still efficiently solvable. In addition, the problem that parameters of the price difference process are never known exactly and are imprecisely estimated from an observed finite sample is investigated (recalling that this problem is critical for practice). It is shown how the imprecision affects the optimal trading strategy by quantification of the loss caused by the imprecise estimate compared to a theoretical trader knowing the parameters exactly. The main results focus on the geometric and optimization-theoretic viewpoint of the risk-bounded trading strategy and the imprecision resulting from the statistical estimates.

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。