EXPLORATIVE STUDY ON DEPENDENCE THROUGH VINE COPULA AND ITS APPLICATION FOR AGGREGATE RISK MEASURE WITH GARCH CLASS MODEL - J.M. Wororomi, Martha
The understanding of inter-variable dependence has become increasingly important across various fields, particularly in quantitative risk management. In general, to determine whether there is dependence, visualization can be done through scatter plots. The inter-variable dependence can be quantitatively measured using correlation measures such as Rho Pearson and Tau Kendall. Furthermore, dependence models are constructed through joint distribution functions and marginal distribution functions. However, when faced with different variable distributions, determining the joint distribution function can be challenging. Copulas can be employed to formulate joint distribution functions when dealing with diverse variable distributions. In this research, the dependence model is constructed for multivariate distributions. For multivariate cases, the dependence model will be constructed using copula vines through a graphical structure known as a Regular Vine (R-Vine). To model dependencies using copula vines, an appropriate vine graph structure is required. Therefore, the most suitable vine graph structure to model the dependence between Bitcoin, Ethereum, Binance Coin, and gold (as a safe-haven) is determined through a numerical algorithm. This dependence is then used to quantify the aggregate risk of the portfolio, modeled using three first-order GARCH class models involving conditional means, specifically first-order ARMA.