Determining the Most Suitable Distribution and Estimation Method for Extremes in Financial Data with Different Volatility Levels

In finance, accurately modelling the tail behaviour of extreme log returns is critical for understanding and mitigating risks across diverse asset classes. This research employs extreme value theory to identify the most suitable probability distributions (i.e., generalized extreme value (GEV), generalized logistic (GLO), Gumbel (GUM), generalized Pareto (GP), and reverse Gumbel (REV)) and estimation methods (least squares (LS), weighted least squares (WLS), maximum likelihood (ML), L-moments (LM), and relative least squares (RLS)) for modelling the tail behaviour of log returns from two financial datasets, each representing a distinct asset class with high (Ethereum, a digital asset class) and low (South African government bonds, a fixed-income asset class) volatility levels. The performance of each model and estimation method (25 different possibilities) is evaluated through goodness-of-fit and risk measures as the study aims to determine the optimal approach for each volatility level. Results from ranking different models and estimation methods show that across both asset classes, ML consistently emerges as the top-performing estimation method across all distributions. LM serves as a solid secondary option, while LS occasionally excels under GLO’s weekly minima for low volatility, whereas RLS occasionally surpasses ML in GLO’s monthly minima for high volatility. Finally, WLS uniquely outperforms under GEV and GLO’s monthly minima under low volatility.