Author(s)

Cyprian O. Omari^1*, Peter N. Mwita², Antony W. Gichuhi³

¹Department of Statistics and Actuarial Science, Dedan Kimathi University of Technology, Nyeri, Kenya.
²Department of Mathematics and Statistics, Machakos University, Machakos, Kenya.
³Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

This paper implements the statistical modelling of the dependence structure of 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 ARMA-GARCH model is used to filter the return series. The generalized Pareto distribution is then fitted to model the tail distribution of standardized residuals. The dependence structure between transformed residuals is 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 copula models.

Backtesting, Copulas, Currency Exchange Rate, Dependence Modelling, GARCH-EVT-Copula Model, Portfolio Risk, Value-at-Risk

Omari, C. , Mwita, P. and Gichuhi, A. (2018) Currency Portfolio Risk Measurement with Generalized Autoregressive Conditional Heteroscedastic-Extreme Value Theory-Copula Model. Journal of Mathematical Finance, 8, 457-477. doi: 10.4236/jmf.2018.82029.