Comparative Analysis of Tail Risk in Emerging and Developed Equity Markets: An Extreme Value Theory Perspective

This research explores the application of extreme value theory in modelling and quantifying tail risks across different economic equity markets, with focus on the Nairobi Securities Exchange (NSE20), the South African Equity Market (FTSE/JSE Top40) and the US Equity Index (S&P500). The study aims to recommend the most suitable probability distribution between the Generalised Extreme Value Distribution (GEVD) and the Generalised Pareto Distribution (GPD) and to assess the associated tail risk using the value-at-risk and expected shortfall. To address volatility clustering, four generalised autoregressive conditional heteroscedasticity (GARCH) models (standard GARCH, exponential GARCH, threshold-GARCH and APARCH (asymmetric power ARCH)) are first applied to returns before implementing the peaks-over-threshold and block maxima methods on standardised residuals. For each equity index, the probability models were ranked based on goodness-of-fit and accuracy using a combination of graphical and numerical methods as well as the comparison of empirical and theoretical risk measures. Beyond its technical contributions, this study has broader implications for building sustainable and resilient financial systems. The results indicate that, for the GEVD, the maxima and minima returns of block size 21 yield the best fit for all indices. For GPD, Hill’s plot is the preferred threshold selection method across all indices due to higher exceedances. A final comparison between GEVD and GPD is conducted to estimate tail risk for each index, and it is observed that GPD consistently outperforms GEVD regardless of market classification.