Volatility Modeling of Currency Returns: A Bayesian Multivariate GARCH-EVT Framework

Exchange rate volatility is widely recognized as a major driver of financial instability in emerging markets, driven by its complex dynamics, time-varying dependence structures, and the frequent occurrence of extreme events. However, existing models often treat these interrelated features in isolation, limiting their ability to adequately capture their joint effects and provide a comprehensive understanding of financial risk. This study addresses this limitation by proposing a unified Bayesian framework that integrates an asymmetric dynamic conditional correlation (ADCC) model, an exponential GARCH (EGARCH) model, and extreme value theory (EVT) to jointly capture volatility persistence, asymmetric and time-varying correlations, and tail risk in a multivariate system of currency returns. The model is estimated using the No-U-Turn Sampler (NUTS), enabling full posterior uncertainty quantification. Using daily data for six currencies (GBP, EUR, CNY, INR, KES, and UGX) against the Rwandan Franc from 2018 to 2022, the results reveal persistent volatility, nearly symmetric shock responses (suggesting limited leverage effects), and correlations that strengthen during joint market downturns. EVT further indicates heavier tail behavior for KES and INR, signaling greater exposure to extreme exchange rate movements. Model comparison based on the widely applicable information criterion (WAIC), leave-one-out cross-validation (LOO-CV), and backtesting shows that the proposed framework outperforms standard DCC-GARCH and BEKK-GARCH models, reducing WAIC by 158.4 and LOO-CV by 173.3 while improving expected shortfall (ES) calibration. The framework provides a practical tool for understanding dynamic interdependencies and extreme risks, supporting more effective stress-testing and exchange rate risk management. It also underscores the importance of adopting dynamic, risk-aware models to improve transaction cost management and guide central bank interventions in emerging markets.