The Extreme Value Copulas Analysis of the Risk Dependence for the Foreign Exchange Data

The aim of this paper is to analyze the dependence structure between the asset returns using the extreme value copulas. We first focus on the use of extreme value theory, more specifically, the generalized extreme distribution (GEV) to model the tail behavior of the financial return series based on monthly maxima and minima of daily USD/UK, USD/EUR foreign exchange data. A parameter estimation based on maximum likelihood method is proposed for the parameter estimation of the GEV model, on the basis of which, we conduct the statistical estimation of the copula parameters using Inference for Margins (IFM) method. We thereafter identify the suitable copulas based on the parametric and nonparametric estimation of the dependence function. The procedure is proposed for the calibration of the copula functions to recover the joint tail distribution and quantify the magnitude of tail dependence by comparing three different extreme value copulas. The results show that three members we concerned are all suitable copulas that have the desired property to measure the joint tail risk and tail dependence for our empirical market data.