Dynamic Volatility and Tail Risk in BTC, BWP, and ZAR Exchange Rates: Bayesian SARMA-GARCH with Skewed Error Distributions

Exchange rate volatility presents significant risks to investors and governments, especially in developing economies and the cryptocurrency market, where unforeseen shocks may lead to considerable financial losses. Standard risk metrics frequently do not account for time-varying volatility, skewness, and fat-tailed return distributions, thereby constraining their predictive reliability. This research utilises a Bayesian SARMA–GARCH methodology with time-varying parameters to evaluate exchange rate risk for BTC/USD, BWP/USD, and ZAR/USD. Daily log returns are modelled with Asymmetric Generalised Error Distributions to address heavy-tailed and skewed characteristics. One-step-ahead forecasts of Value-at-Risk (VaR) and Expected Shortfall (ES) are produced and systematically backtested employing credible intervals, weighted continuous ranking probability scores, and dynamic quantile tests. The findings demonstrate substantial predictive accuracy, with Mean Prediction Interval Widths of 0.0518 for BTC/USD, 0.0722 for BWP/USD, and 0.0413 for ZAR/USD, and the majority of observed returns remaining within the 99\% prediction intervals. BTC/USD responds rapidly to disturbances, ZAR/USD demonstrates persistent volatility, and BWP/USD reflects extended effects. The integration of time-varying dynamics and heavy-tailed distributions enhances the reliability of Value at Risk (VaR) and Expected Shortfall (ES) forecasts, thereby facilitating improved risk management, portfolio allocation, and regulatory oversight.