Copulas and Correlation in Statistical Risk Theory

Abstract

The Financial Risk Management (FRM) aims to identify, measure and manage risks in different sectors. One of the core things during such operations is measuring different dependencies. Linear correlation is known as one of the most popular measure of dependence, however it is known that it is a reasonable mea- sure of dependence only when variables are Normally distributed, but this is not the case with credit and portfolio risks, therefore other measures of dependency are needed. This paper presents a Copula function for bivariate case as one of the tools to analyze dependencies in portfolio risk management. Copulas were first introduced by Sklar in 1959 [8], and in 1999 they were studied in financial context for the first time by Embrechts et al. in 1999 [4]. Motivated by the copula analysis of European stock portfolios [6], this paper aims to analyze portfolio consisting of Asian S&P Asia 50 and S&P BSE 100 indices, and apply copula to this portfolio.