Estimation and Simulation of Copula Function: An Application to Daily Korean Treasury and A-Rated Corporate Spot Rates

A Copula function is an useful tool for constructing and simulating multivariate distributions. It relates one-dimensional marginals with multi-dimensional distribution. By doing so, one can separately model the distribution of individual series and the dependence structure and the estimation becomes a much simpler problem. As such, data simulated from a copula allows one to price complex financial products that would be impossible otherwise and to measure both market and credit risks more realistically and accurately. This paper intends to summarize the copula methodology and applies it to the problem of simulating default-free and risky spot rates. More specifically, this paper estimates the dependence structure of daily Korean Treasury and A-rated corporate spot rates (3-year to maturity) for the 1/2/01~11/11/02 period using t-marginals and bivariate t-copula. The data appear to support the empirical fact that these rates have fat-tails and t_(3.7)-copula seems to be the reasonable description of the daily changes in spot rates. This paper also demonstrates the simulation of the data from t_(3.7)-copula.