Abstract
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.
Highlights
The currency exchange market plays an important role in evaluating the performance of the country’s economy and the stability of its financial system
The backtesting results demonstrate that the semi-parametric approach provide accurate estimates of portfolio risk on the basis of statistical coverage tests compared to benchmark copula models
For a given asset or portfolio of financial assets, probability and time horizon, VaR is defined as the worst expected loss due to change in value of the asset or portfolio of financial assets at a given confidence level over a specific time horizon under the assumption of normal market conditions and no transaction costs in the assets
Summary
The currency exchange market plays an important role in evaluating the performance of the country’s economy and the stability of its financial system. The ever increasing uncertainties in the financial markets have motivated practitioners, researchers and academicians to develop new and improve existing methodologies applied in financial risk measurement. For a given asset or portfolio of financial assets, probability and time horizon, VaR is defined as the worst expected loss due to change in value of the asset or portfolio of financial assets at a given confidence level over a specific time horizon (typically a day or 10 days) under the assumption of normal market conditions and no transaction costs in the assets
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