Modelling the Dependence Structure of Financial Assets: A Bivariate Extreme Data Study

Abstract

Quantifying dependence among variables is the core of all modelling efforts in financial econometrics. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. In order to predict extreme losses in finance, extreme value copulas play more important role than copulas. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data and introducing a negative dependence between the assets return. This model was applied in the portfolio of the IDX Composite Index (IHSG) and the exchange rate for Indonesia Rupiah to United States Dollar (NT). Each individual asset return is modelled by the AR-GARCH and the joint distribution is modelled using extreme value copulas. As a comparison, the joint distribution is also modelled using the copulas. The result shows that the dependence between IHSG and NT is negative. Therefore, in this paper, we tested the extreme value copulas and the copulas which were rotated 270 degree and 90 degree. The empirical study showed that the extreme value copulas rotated with 270 degree are relatively more appropriate model than the copulas. Quantifying dependence among variables is the core of all modelling efforts in financial econometrics. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. In order to predict extreme losses in finance, extreme value copulas play more important role than copulas. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data and introducing a negative dependence between the assets return. This model was applied in the portfolio of the IDX Composite Index (IHSG) and the exchange rate for Indonesia Rupiah to United States Dollar (NT). Each individual asset return is modelled by the AR-GARCH and the joint distribution is modelled using extreme value copulas. As a comparison, the joint distribution is also modelled using the copulas. The result shows that the dependence between IHSG and NT is negative. Therefore, in this paper, we tested the extreme value copulas and the copulas which were rotated 270 degree and 90 degree. The empirical study showed that the extreme value copulas rotated with 270 degree are relatively more appropriate model than the copulas.