Using Dynamic Copulae for Modeling Dependency in Currency Denominations of a Diversifed World Stock Index

Abstract

The aim of this paper is to model the dependency among log-returns when security account prices are expressed in units of a well diversified world stock index. The paper uses the equi-weighted index EWI104s, calculated as the average of 104 world industry sector indices. The log-returns of its denominations in different currencies appear to be Student-t distributed with about four degrees of freedom. Motivated by these findings, the dependency in log-returns of currency denominations of the EWI104s is modeled using time-varying copulae, aiming to identify the best fitting copula family. The Student-t copula turns generally out to be superior to e.g. the Gaussian copula, where the dependence structure relates to the multivariate normal distribution. It is shown that merely changing the distributional assumption for the log-returns of the marginals from normal to Student-t leads to a significantly better fit. Furthermore, the Student-t copula with Student-t marginals is able to better capture dependent extreme values than the other models considered. Finally, the paper applies copulae to the estimation of the Value-at-Risk and the expected shortfall of a portfolio, constructed of savings accounts of different currencies. The proposed copula-based approach allows to split market risk into general and specific market risk, as defied in regulatory documents. The paper demonstrates that the approach performs clearly better than the Risk Metrics approach.

Keywords: diversified world stock index, Student-t distribution, time-varying copula, Value-at-Risk, expected shortfall