Modelling extreme stock market returns using Hawkes and Poisson processes

Sammanfattning

In probability theory, the assumption of independence between consecutive events is strong. However, when analyzing empirical data, this assumption is often weak or violated. This thesis investigates whether extreme negative daily returns in stock indices occur independently over time. To address this question, self-exciting Hawkes models are applied to extreme negative returns in two stock indices, the S&P 500 and OMXS30, over a 15-year period. A Poisson process is fitted to the same data as a baseline model. Model performance is evaluated using goodness-of-fit tests and Akaike’s Information Criterion (AIC). Since the data are observed on a discrete time scale while the evaluation methods are developed for continuous-time processes, a simulation study is conducted. The results show that Lilliefors-corrected critical values yield an overly liberal Kolmogorov–Smirnov test when applied to a discrete Poisson process. In contrast, bootstrapped critical values provide a more accurate and powerful testing procedure. The empirical results show that the Hawkes process provides a better fit to extreme negative daily returns than the Poisson process, indicating the presence of temporal dependence and clustering in extreme market events. The findings further suggest that an extreme negative return induces a larger immediate shock to the event intensity in the larger and more liquid market, while the impact decays more slowly and persists longer in the smaller, less liquid market.