Thesis submitted in partial fulfillment of the requirements for the Degree of Master of Science in Statistical Sciences (MSc.SS) at Strathmore UniversityBackground: Dependence structure is used widely to describe relationships between risks and provides estimation of risks for risk management purposes. Modeling dependence
structure of stock returns is a difficult task when returns are having non elliptical distributions. Objective: To examine the dependence pattern between the Kenya stock market return and BRICS stock market returns. Methods: In this dissertation, we estimated the dependence using copula GARCH, an approach that combines copula functions and GARCH models. We applied this method to a stock market returns consisting of stock indices of Brazil, Russia, India, China and South Africa (BRICS) and Kenya stock market. We first used GARCH(1,1) to model the marginal distributions of each stock returns using different GARCH(1,1) specifications. Copula was then used to analyze the dependence between the BRICS stock market returns and Kenya stock market returns using the standardized marginal distributions derived from GARCH(1,1) residuals. The best fitting copula parameter was determined using the log likelihood or AIC.Results: Empirical results showed that GJR-GARCH model provided the best fit for Brazil, Russia, China and Kenya while E-GARCH model provided the best fit for India and South Africa. As for modeling the dependence structure, student t copula parameter provided the best fit for the marginal distributions of the returns. Conclusion: Marginal models showed presence of volatility clustering which vanishes after crisis. To capture the dependence structure for bi variate data sets, Student t copula was considered to be the appropriate copula function. Recommendation: Further research should be extended to examine the multivariate structure, a joint distribution of BRICS in terms of Multivariate GARCH. Also research should focus on specific time periods in order to ensure effectiveness in measurement and management of risks
