Hawkes-Heston models and their application to high frequency financial data

Abstract

This dissertation investigates the modelling of financial time series through the integration of two well-established frameworks: the Hawkes process and the Heston stochastic volatility model. The resulting Hawkes-Heston diffusion model captures both the continuous evolution of asset prices and the discrete, self-exciting nature of jumps, offering a more flexible structure for analysing high-frequency financial data. Using Tesla Inc. as a case study—due to its pronounced volatility and eventdriven price behaviour this work applies multiple variations of the Hawkes-Heston model, where jumps may appear in the price process, the volatility process, or both. The parameters of each model are estimated using high-frequency intraday data, with jumps detected and removed using the non-parametric L-estimator. Simulations based on the fitted models are used to compute risk measures such as Value at Risk (VaR) and Expected Shortfall (ES), allowing for performance comparisons across the model variations. For benchmark comparisons, VaR and ES results based on an estimated Heston model are also considered. The results provide insights into the dynamic interplay between continuous volatility and discrete jumps and demonstrate the practical utility of Hawkes-driven diffusions in financial risk modelling. It also is concluded that Hawkes-driven diffusions provide similar measures of risk while, surprisingly, Heston model-based risk measures are more conservative due overcompensation in the diffusion term.