Application of Volatility and Extreme Value Theory in Exchange Rate Risk Estimation

Abstract

The importance of conditional Value-at-Risk and conditional Expected Shortfall to estimate extreme risk in financial time series data cannot be exaggerated. This study applies these tools to estimate extreme risk in exchange rate returns. Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is applied to estimate the current volatility in daily exchange rate returns over the period of 10 years and Extreme Value Theory (EVT) approach to estimate quantiles of innovations. First, Autoregressive (AR) model is fitted with GARCH errors to the daily exchange rate returns using Quasi-Maximum likelihood Estimate (Q-MLE) to get the current volatility. Second, Generalized Pareto Distribution (GPD) approach is fitted to the excess returns assuming the residuals are independent and identically distributed. The asymptotic properties of the estimators are given. Finally, the estimated volatility and estimated quantiles are combined to obtain Conditional Value at Risk and Conditional estimates. Results are applied to real data to estimate extreme risk in Rwanda exchange rate process.