A Simple Microstructure Model Based on the Cox-BESQ Process With Application to Optimal Execution Policy

We develop a microstructure model whose order ow is driven by a Cox-BESQ process. We derive important analytical properties of the Cox-BESQ process in order to explicit the stock price dynamics at different time scales, provide different parameter estimators and solve the optimal execution problem. We implement the model using a large data set of stock index and bond futures. Our results show that the Cox-BESQ process provides an alternative framework to the Hawkes process to build a microstructure model that is very exible and has an explicit solution