Hawkes processes and some financial applications

• Main Author: Lapham, Brendon M
• Other Authors: MacDonald, Iain L
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2014
• Online Access: http://hdl.handle.net/11427/8523

Includes bibliographical references. === The self-exciting point process, which is now more commonly known as the Hawkes process, is a model for a point process on the real line introduced by Hawkes (1971). The distinguishing feature of such processes is that they allow all past `events' to affect the intensity function at the current time. Over the years such processes have been applied in seismology and neurophysiology in particular, and in more recent years there have been significant financial applications. In almost all of these applications, the route used to find the maximum likelihood estimates (MLEs) is direct numerical maximisation (DNM) of the likelihood. An EM algorithm, which makes use of the Poisson cluster process interpretation of the Hawkes process, is an alternative route to the MLEs. This particular EM algorithm has received attention in the literature and has been claimed to have advantages over DNM of the likelihood. We carry out a simulation study for a simple Hawkes process to clarify statements made in the literature about these advantages. For the simple Hawkes process models that we consider, DNM of the likelihood is the preferable route to finding the MLEs. We then use DNM of the likelihood to _t marked Hawkes process models to South African asset data. These applications to South African data include the modelling of extreme asset returns and the forecasting of conditional value-at-risk (VaR) and expected shortfall (ES). The models investigated include mostly models found in the literature, but also include some variations introduced here. In a backtesting exercise, we compare the conditional VaR and ES forecasts found by using the marked Hawkes process models with those found via some nonstandard stochastic volatility (SV) models. We find that the marked Hawkes process models give mostly competitive forecasts of conditional VaR and ES when compared with the nonstandard SV models.