Non-parametric estimation of quadratic Hawkes processes for order book events
提出了一种实用的校准方法，用于订单簿事件（市价单、限价单、撤单）的二次霍克斯模型，发现反馈核函数由对角项和秩一Zumbach项组成，且系统接近临界点。
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 slightly stronger feedback kernels would lead to endogenous liquidity crises.