Bayesian Modelling of Tail Risk Using Extreme Value Theory with Application to Currency Exchange

Abstract

Modelling financial tail risk such as investment or financial risk is important to avoid high financial shocks. This study adopted Bayesian techniques to complement the classical extreme value theory (EVT) models to model the exchange rate risk of Nigeria against the South African ZAR. Hence, this study proposed the Bayesian Generalized Extreme Value (BGEV) model, Bayesian Generalized Pareto distribution (BGPD), Bayesian Gumbel (BG), and classical Generalized Pareto distribution (GPD) to fit the exchange rate returns over one hundred and four observations. The model selection criteria were used to determine the best model, consequently, the model selection criteria were in favour of BGEV model. The Value-at-Risk (VaR) and the Expected Shortfall (ES) were obtained from the estimated parameters. The results show that the Nigeria Naira exchange will experience losses against the ZAR both at 95% quantile and 99% quantile. This study recommends that investors should watch closely before making financial or investment decisions. This study aligns with the sustainable development goals (SDGs), 8.1 (sustainable economic growth), SDG 8 (Promote sustained, inclusive and sustainable economic growth).