Copula Estimation for Nonsynchronous Financial Data

Abstract

Copula is a powerful tool to model multivariate data. We propose the modelling of intraday returns of multiple financial assets through copula. The problem originates due to the asynchronous nature of intraday financial data. We propose a consistent estimator of the correlation coefficient in case of elliptical copula and show that the plug-in copula estimator is uniformly convergent. For non-elliptical copulas, we capture the dependence through Kendall’s Tau (leveraging the relation between copula parameter and Kendall’s tau). We demonstrate underestimation of the copula parameter and propose an alternative method to obtain an improved estimator. In simulations, the proposed estimator reduces the bias significantly for a general class of copulas. We apply the proposed methods to real data of several stock prices.