Measuring Contemporaneous Correlation between Return Shock and Volatility Shock in an EGARCH Model

Abstract

GARCH type models, with one disturbance to the return of a financial asset, have not been considered as a framework for measuring the contemporaneous correlation between the return shock and the volatility shock. We show that the contemporaneous correlation can be quantified within an EGARCH model, where the composite disturbance to the return follows a normal log-normal mixture distribution that accommodates skewness and excess kurtosis. The strict stationarity and covariance stationarity of the proposed model are analyzed. The estimation of the model with the SP500 excess return series lends a mild support for the contemporaneous correlation being negative and the ARCH-M effect being positive.

Keywords: GARCH, stochastic volatility, ARCH-M, leverage, maximum likelihood

JEL Classification: C22, C51, G12