论文标题
非参数估算订单簿事件的二次霍克斯流程
Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events
论文作者
论文摘要
我们为一般二次霍克斯订单事件模型（市场订单，限制订单，取消）提出了可操作的校准程序。这种模型的主要特征之一是不仅要编码过去事件对未来事件的影响，而且至关重要的是，过去价格变化对此类事件的影响。我们表明，经验校准的二次内核通过对角线贡献（捕获过去实现的波动率）以及排名第一的“ Zumbach”贡献（捕获过去趋势的效果）很好地描述了。我们发现Zumbach内核和所有其他反馈内核都是时间的幂律。与以前的许多研究一样，发现真正的外源性事件的速率是总事件率的一小部分。这两个功能表明，该系统接近一个关键点 - 从某种意义上说，更强的反馈内核会导致不稳定性。
We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.
