Currency Portfolio Risk Measurement with Generalized Autoregressive Conditional Heteroscedastic-Extreme Value Theory- Copula model

Abstract

This paper implements the statistical modelling of the dependence structure of bivariate currency exchange rates using the concept of copulas. The GARCH-EVT-Copula model is applied to estimate the portfolio Value-at-Risk (VaR) of currency exchange rates. First the univariate ARMAGARCH model is used to filter the return series. The generalized Pareto distribution is then fitted to the tails of the standardized residuals to model the distributions marginal residuals. Dependences between transformed residuals are modeled using bivariate copulas. Finally the portfolio VaR is estimated based on Monte Carlo simulations on an equally weighted portfolio of four currency exchange rates. The empirical results demonstrate that the Student’s t copula provide the most appropriate representation of the dependence structure of the currency exchange rates. The backtesting results also demonstrate that the semi-parametric approach provide accurate estimates of portfolio risk on the basis of statistical coverage tests compared to benchmark GARCH models. Keywords: Backtesting, copulas, currency exchange rate, dependence modelling, GARCH-EVTCopula model, portfolio risk, Value-at-Risk.