Modeling financial markets using copula functions

Abstract

This paper presents an analysis of copula models in comparison to standard statistical distributions in the context of international securities markets. Due to the fact that copula models require independent and identically distributed (i.i.d.) random variables, the market data is transformed into log-returns, and then filtered using ARIMA-GARCH time series methods. Once the market data is put into an appropriate form, it is fit to several standard statistical distributions, as well as more non-conventional copula distributions. The dependance structure of the distributions are analyzed in order to determine which model would be most appropriate in the context of quantiative finance. The goal of the paper is to show that copulas can model extreme market relations better than the traditional distributions that are currently being used in finance.