Modelling rare events in finance

Understanding the dynamics of asset prices, exchange rates, and other financial time series has posed a persistent challenge for economists, financial mathematicians, and market practitioners. Traditional models, such as the plain or geometric random walk, have proven inadequate, particularly when it comes to capturing extreme events—large, sudden price movements that occur far more frequently than predicted by standard Gaussian models. These extreme events, which manifest as significant market gains or losses, highlight the limitations of traditional approaches and underscore the need for more robust modelling techniques.

Despite being recognized for over 70 years, the quest to develop alternative models that comprehensively explain the salient features, or ‘stylised facts,’ of real-world financial data remains ongoing. These stylised facts include heavy-tailed distributions, volatility clustering, and extreme correlations, which are critical for understanding the behaviours of financial systems under stress. However, with the advent of large, fully time-resolved financial datasets and the rapid advancement of machine learning and computational techniques, we are now in a unique position to make substantial progress in this area.

This PhD project is aimed at advancing the understanding of extreme events in financial markets, focusing on their occurrence, correlation, and impact. The project will utilize adaptive multilevel splitting and Monte Carlo simulations to explore the extreme phenomena in high-dimensional systems. By applying these approaches to financial datasets, particularly those linked to derivatives that respond to extreme market or natural events, the successful candidate will gain new insights into the mechanics of rare events and their effects on market stability and can capture the behaviour of financial markets under both normal and extreme conditions.

Funding notes:

This is PhD project is open to students worldwide, and the funding will cover UK home fees plus stipend. For details of the funding avaiable and advice on making your application, please contact: [email protected]