Application of three-dimensional copula functions in the analysis of dependence structure between exchange rates
Application of three-dimensional copula functions in the analysis of dependence structure between exchange rates

Summary/Abstract: The multivariate analysis of financial data has gained a lot of attention. Investors are no longer interested in knowing only the dependence between two components of their portfolio but between all of them as it allows them to better understand andto assess the situation on the financial market. Copula functions seem to be a tool efficient enough to provide deep and understandable results regarding instruments dependence. This paper has a goal to analyze the relation between three currencies: USD, EUR and CZK against PLN. The literature research has shown that such analyses are performed but the use of elliptical copulas, namely normal and t-Student copula functions dominate. Another disadvantage is that instruments are grouped in pairs enabling a bivariate analysis. Multivariate approach can simplify calculations and lead to more reliable results. However, multivariate copula models are still under deep investigtion. Therefore another approach has been proposed: a decomposition of a joint multivariate distribution function into a product of marginal densities functions and a pair copula density function. In this paper, we will focus on Archimedean copula functions such as the Frank, Clayton and Gumbel families which constitute an introduction to multivariate analysis of financial underlying instruments.

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