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用于建模金融微观结构噪声的霍克斯过程

文章 arXiv papers · 作者: E. Bacry et al.
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总结

这项研究使用带标记点过程和自激、互激霍克斯强度，对资产价格的逐笔变化建模。研究用不同的计数过程表示正向和负向价格跳跃。通过耦合单个资产或一对资产的向上与向下事件强度，模型捕捉短期均值回归和埃普斯效应（收益相关性在较精细的时间尺度上减弱），同时在较长时间范围内保留类似布朗运动的特征。

作者推导了平均特征图以及两个价格增量之间相关性的闭式表达式，从而可以分析不同尺度下从均值回归到扩散的转变。作者报告称，在多种设定下，理论结果与 Euro-Bund 期货和 Euro-Bobl 期货的实证拟合一致。摘录未提供拟合细节，也未证明该模型可推广到这些合约和情形之外。

核心观点

  • 模型用带标记计数过程表示价格向上和向下跳跃。
  • 自激和互激的霍克斯强度将资产内部及资产之间的价格事件联系起来。
  • 耦合强度再现了短期均值回归和埃普斯效应。
  • 闭式结果描述了不同时间尺度下的特征图和跨资产增量相关性。
  • 研究报告了对 Euro-Bund 期货和 Euro-Bobl 期货的实证拟合。

标签

期货市场微观结构统计学均值回归
全文
# Modeling microstructure noise with mutually exciting point processes


# Modeling microstructure noise with mutually exciting point processes









We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.

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。