On a Hybrid Clayton-Gumbel and Gumbel-Frank Bivariate Copulas with Application to Stock Indices

International audience The study proposes two convex convolution based bivariate Archimedean copulas with their joint distribution functions and conditional distribution functions. Several simulations were performed using sample sizes 100,1000, 10000 and 1000000 for combinations of distributions: Gamma and exponential, Normal and exponential, Gamma and normal, Chi-square and Poisson as well as Skew normal and skew normal for the pairs of random variables to assess the performance of the models under different pairs of distributions. Using the method of maximum likelihood estimation, estimates were obtained for the likelihood function and used in obtaining Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for comparison of the proposed copula models with existing copula models. The models were applied to two listed stocks on the Ghana Stock Exchange. In all, the proposed models, Clayton-Gumbel and Gumbel-Frank outperformed the existing models.