Modelling dependence structure for financial risk: A copula approach

Copula distributions are frequently being used in financial studies. The reason of this preference is that unlike correlation based models, copulas provide a comprehensive approach to interpret the dependence structures. Financial time series have heavy tailed characteristics and volatility. This situation requires a copula approach to analyze a market's dependence structure and forecast its risks while considering extremes. Also, joint behaviour of multiple markets hence multiple investment potentials can be examined without the concern of marginal distributions with the help of copulas. In order to clarify the risks of an investment, financial structure of the targeted market requires sensitive modeling that acknowledges the volatile nature. Value-at-Risk (VaR) models help the investors to forecast the consequences of the investment for a particular market. In this study, we explicitly analyze the relation between changes in oil prices and stock market returns for emerging markets. Our goal is to investigate how Brent oil and emerging markets are affected by each other and compute risk measures for these two assets. All datasets are tested via goodness of fit test to determine proper copula distributions. We propose to forecast the Value-at-Risk of the portfolios on the basis of bivariate copulas using nonparametric estimates of the coefficient of tail dependence which is estimated to fit the data according to its extreme observations. Changes in tail dependence by time are visualized by comparing parametric and non-parametric estimations through a simulation study. Then, VaR for the scenario of equally weighted assets are computed by simulating cumulative returns. Furthermore, validity of VaR models are tested by applying backtesting. Lastly, Conditional Value-at-Risk (CoVaR) estimation is carried out to observe market dynamics when Brent market is under stress.