High-frequency financial data modeling using Hawkes processes

Intraday Value-at-Risk (VaR) is one of the risk measures used by market participants involved in high-frequency trading. High-frequency log-returns feature important kurtosis (fat tails) and volatility clustering (extreme log-returns appear in clusters) that VaR models should take into account. We propose a marked point process model for the excesses of the time series over a high threshold that combines Hawkes processes for the exceedances with a generalized Pareto distribution model for the marks (exceedance sizes). The conditional approach features intraday clustering of extremes and is used to calculate instantaneous conditional VaR. The models are backtested on real data and compared to a competitor approach that proposes a nonparametric extension of the classical peaks-over-threshold method. Maximum likelihood estimation is computationally intensive; we use a differential evolution genetic algorithm to find adequate starting values for the optimization process.