Estimation of Value at Risk in the Presence of Dependence Structure in Financial Returns: A Copula Based Approach

Modeling dependence structure in financial economics is of paramount importance when estimating portfolio’s value at risk, since risk of an asset in addition to its own behavior is also dependent on the behavior of other assets in the portfolio. Application of joint distribution Copula is one of the methods for incorporation dependence at lower and upper tail of returns’ distribution in financial economics. Copulas are functions that connect multivariate distribution function to their marginal distribution. In the current study, the dependence structure among two price indexes for chemical and pharmaceutical products of TEPIX between 3/1/2005 – 18/3/2013 was evaluated by combining different types of Copula functions and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. In addition, the effect of dependence structure on estimation of comprised portfolio’s value at risk is investigated. Empirical results of this study demonstrate that there is asymmetric dependence structure between chemical and pharmaceutical products of TEPIX indexes. Furthermore, the results indicate that Copula-GARCH approach is more accurate and efficient compared to commonly used models such as M-GARCH, DCC-GARCH, EWMA, and historical simulation methods in estimation of portfolio’s value at risk