High-dimensional Hawkes processes for limit order books: modelling, empirical analysis and numerical calibration
用指数核的高维霍克斯过程描述订单驱动市场的限价订单簿，基于实证分析建模订单间依赖关系，发现抑制效应并引入非线性霍克斯过程，解决高维校准难题，模型与数据统计性质吻合良好。
High-dimensional Hawkes processes with exponential kernels are used to describe limit order books in order-driven financial markets. The dependencies between orders of various types are carefully studied and modelled, based on a thorough empirical analysis. The observation of inhibition effects is particularly interesting, and leads us to the use of non-linear Hawkes processes. Specific attention is devoted to the calibration problem, in order to account for the high dimensionality of the problem and the very poor convexity properties of the MLE. Our analyses show a good agreement between the statistical properties of order book data and those of the model.