从二次Hawkes过程到具有Zumbach效应的超Heston粗糙波动率模型
From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect
摘要：
利用基于Hawkes过程的微观价格模型，证明了在一定的无套利条件下，市场的高度内生性和元序分裂现象在宏观尺度上产生了粗糙的Heston型波动.金融动力学的另一个重要特征是所谓的反馈或Zumbach效应，它是经济物理学中几部有影响力的著作的核心。这基本上意味着过去的回报趋势传达了未来波动的重要信息。在微观结构建模中再现这种性质的一种自然方法是使用霍克斯过程的二次版本。我们发现，经过适当的重新缩放，这些过程的长期限制是粗糙赫斯顿模型的改进版本，其中的波动系数相比，赫斯顿型动力学的平方根特征增强。此外，Zumbach效应在这些有限的粗糙波动率模型中仍然是明确的。
英文摘要：
Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage condition, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generate rough Heston-type volatility at the macroscopic scale. One additional important feature of financial dynamics, at the heart of several influential works in econophysics, is the so-called feedback or Zumbach effect. This essentially means that past trends in returns convey significant information on future volatility. A natural way to reproduce this property in microstructure modeling is to use quadratic versions of Hawkes processes. We show that after suitable rescaling, the long term limits of these processes are refined versions of rough Heston models where the volatility coefficient is enhanced compared to the square root characterizing Heston-type dynamics. Furthermore the Zumbach effect remains explicit in these limiting rough volatility models.
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