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Title: A GARCH-Hawkes jump model: Self-excitation and calibration Authors:  Jing Chen - Cardiff University (United Kingdom)
Steve Yang - Stevens Institute of Technology (United States)
Alan Hawkes - Swansea University (United Kingdom) [presenting]
Abstract: With consideration of increased observations on contagion effects of market events occurring in financial markets, it is argued that classic diffusion models and/or their extension incorporating Poisson or Levy jumps are not sufficient to best describe the non-linearity of financial time series. Instead, we propose to incorporate an intensity based model and the simplest but most effective choice is a one-dimension Hawkes process self-excitation. Our aim is to establish such a model with practicality that leads us to focus on calibrating the Hawkes jump model and comparing its effectiveness with the NGARCH model, experimenting over a long period of intraday price series of S\&P 500. During the model estimation, we use a Monte Carlo EM algorithm to achieve the optimisation and overcome the issue of obtaining the marginal distribution of unobserved data. We also use a simulated annealing optimisation algorithm to further enhance the optimisation process. Finally, we compare the Heston and Hawkes models to validate our proposal through better achieved model parameters without digging into complicated option pricing or establishing volatility forecasting.