A multivariate Heston-Hawkes jump diffusion with application to high-frequency big tech stock prices

Abstract

The tech industry has witnessed significant growth and disruption in recent years. Indeed, tech giants such as Apple, Meta and Microsoft play pivotal roles in the reshaping of traditional tech services. Investments in these tech giants are continuously evolving, where market dynamics are constantly influenced by real-time information. Understanding these dynamics is essential as these companies are rather significant in the market, due to their large market capitalisation. Furthermore, changes in the stock prices can signal shifts in technological trends and market perceptions of future developments. Taking this into consideration, this dissertation investigates the dynamic relationships between the stock prices of these big tech companies using a combination of the multivariate Hawkes process and the multi-asset Heston model. By utilising intraday data, the study explores the notion of jumps and volatility of an asset affecting not only the future values of the asset price itself, however also those for other assets. Theoretical foundations are laid out in chapters focusing on the d-dimensional Hawkes process, the d-asset Heston model, and a non-parametric jump-identification technique called the L-estimator. Furthermore, stock prices are analysed pairwise, by initially identifying the occurrences of jumps and fitting a bivariate Hawkes model on these jumps, followed by disentangling said jumps to obtain the continuous part of the data, in order to fit a two-asset Heston model on this data, thereby studying the stochastic volatility endured by the assets in question. The models fitted highlight that jumps are indeed mutually exciting, stochastic volatility is at its peak when the price is at its minimum, and that each of the asset price and volatility processes for AAPL, META and MSFT are moderately correlated, as anticipated.