In this seminar, I will talk about generative models based on point processes for financial time series simulation. Specifically, we focus on a recently developed state-dependent Hawkes (sdHawkes) process to model the limit order book dynamics [Morariu-Patrichi, 2018]. The sdHawkes model consists of an oracle Hawkes process and a state process following Markov transition. The Hawkes and state processes are fully coupled, which enables the point process captures the self- and cross-excitation as well as the interaction between events and states. We will go through the model formulation in sdHawkes, the simulation of sdHawkes, its maximum likelihood estimation, and more importantly, its application to high-frequency data modeling that captures the interactions between the order flow and the state of the current market.

Morariu-Patrichi, Maxime, and Mikko S. Pakkanen. "State-dependent Hawkes processes and their application to limit order book modelling." arXiv preprint arXiv:1809.08060 (2018).