Hawkes process modelling of financial jumps A volatility forecasting approach

Pierre, Sébastien 2024. Hawkes process modelling of financial jumps A volatility forecasting approach. PhD Thesis, Cardiff University. Item availability restricted.

Preview	PDF - Accepted Post-Print Version Download (5MB) | Preview
	PDF (Cardiff University Electronic Publication Form) - Supplemental Material Restricted to Repository staff only Download (1MB)

Abstract

Volatility modeling has been a subject of interest for researchers over the past decades, particularly since the availability of high-frequency financial data. The forecasting accuracy of volatility models has direct implications to the performance of market practitioners, such as volatility traders and risk managers. This thesis introduces original Heterogeneous Autoregressive (HAR) volatility model specifications using jump components expressed as Hawkes intensities. The main research contributions are threefold. Standard financial jump detection methods, such as the Barndorff-Nielsen Shephard (BNS) and the Andersen Bollerslev Dobrev (ABD) methods, use continuous variation and quarticity for the computation of their respective jump detection statistics. Microstructure noise inherent to financial data tends to create biases in continuous variation estimates. A first research contribution is the formulation of alternative measures of continuous variation and quarticity, which effectively neutralize these statistical biases. These new measures lead to more coherent jump detection rates across a wide range of financial asset profiles. The computation of Hawkes jump intensities is performed using a Maximum Likelihood (MLE) approach. Hawkes process parameters are optimized to best fit the timing of detected jump events. Due to the complexity of the problem, MLE is estimated using numerical optimization techniques. Successful convergence of the optimization algorithm to a near-global solution minimizes measurement errors in the Hawkes intensities. To this end, this research formulates original hybrid algorithms, constituted of a modified bionomic (MB) global search engine with its solutions locally improved by either a Nelder Mead (NM) or an Expectation Maximization (EM) algorithm. A third contribution is the introduction of original extensions to the HAR volatility model. It is shown that financial jumps carry significant predictive power for the forecasting of next-day volatility. Moreover, the distinction between upward and downward jumps is suggested, with results indicating that upward jump components carry more predictive power than downward jumps.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Date of First Compliant Deposit:	13 May 2025
Last Modified:	13 May 2025 18:30
URI:	https://orca.cardiff.ac.uk/id/eprint/178251

Actions (repository staff only)

Edit Item