Extreme Value Theory and Risk Quantification in the Nigerian Banking Sector During Financial Stress Periods

This study applies extreme value theory to quantify tail risks in the Nigerian banking sector, estimating value-at-risk and expected shortfall for a composite index of banking sector equity returns during identified periods of financial stress, including the 2016 recession, the 2020 COVID-19 market dislocation, and the 2022 to 2023 naira devaluation and currency reform episodes. Extreme value theory offers a statistically principled framework for estimating the probability and magnitude of severe financial losses in the distributional tails, where standard normal or Student-t assumptions used in parametric risk models consistently understate risk. Daily total return data for the Nigerian Exchange Group banking sector index from January 2014 to December 2023 are analysed, with block maxima and peaks-over-threshold methods applied to model extreme negative return events. Generalised extreme value and generalised Pareto distributions are fitted to extreme return observations, and parameters are estimated using maximum likelihood with bootstrap confidence intervals. Value-at-risk and expected shortfall estimates at the 99th and 99.9th percentile confidence levels are compared against estimates from conventional parametric approaches to quantify the underestimation of tail risk by standard methods. Backtesting using the Kupiec proportion of failures test and the Christoffersen conditional coverage test validates the out-of-sample performance of the extreme value estimates. Results confirm that generalised Pareto-based expected shortfall estimates are systematically higher than parametric benchmarks during stress periods. Keywords: extreme value theory, value-at-risk, generalised Pareto distribution, banking sector risk, Nigeria