Using Conditional Extreme Value Theory to Estimate Value-at-Risk for Daily Currency Exchange Rates

Abstract

This paper implements different approaches used to compute the one-day Value-at-Risk (VaR) forecast for a portfolio of four currency exchange rates. The concepts and techniques of the conventional methods considered in the study are first reviewed. These approaches have shortcomings and therefore fail to capture the stylized characteristics of financial time series returns such as; non-normality, the phenomenon of volatility clustering and the fat tails exhibited by the return distribution. The GARCH models and its extensions have been widely used in financial econometrics to model the conditional volatility dynamics of financial returns. The paper utilizes a conditional extreme value theory (EVT) based model that combines the GJR-GARCH model that takes into account the asymmetric shocks in time-varying volatility observed in financial return series and EVT focuses on modeling the tail distribution to estimate extreme currency tail risk. The relative out-of-sample forecasting performance of the conditional-EVT model compared to the conventional models in estimating extreme risk is evaluated using the dynamic backtesting procedures. Comparing each of the methods based on the backtesting results, the conditional EVT-based model overwhelmingly outperforms all the conventional models. The overall results demonstrate that the conditional EVT-based model provides more accurate out-of-sample VaR forecasts in estimating the currency tail risk and captures the stylized facts of financial returns.