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Journal of Financial Econometrics Advance Access published online on December 9, 2008
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbn017
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

The Impact of Shocks on Higher Moments

Eric Jondeau
     Swiss Finance Institute and University of Lausanne

Michael Rockinger
     Swiss Finance Institute, University of Lausanne, and CEPR

Address correspondence to Michael Rockinger, Swiss Finance Institute, University of Lausanne, and CEPR. Faculty of Business and Economics, University of Lausanne. CH 1012 Lausanne, Switzerland, or e-mail: michael.rockinger{at}unil.ch

JEL Classification: C22, C51, G12


  Abstract

In this paper, we extend the concept of the news impact curve of volatility developed by Engle and Ng (1993) to the higher moments and co-moments of the multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model with non-normal innovations. For this purpose, we present a new methodology to describe the joint distribution of GARCH processes in a non-normal setting. Then, we provide expressions for the response of the moments of the subsequent distribution to a shock. This tool enhances the understanding of the temporal evolution of the joint distribution. We use our methodology to provide stylized facts for the four largest international stock markets. In particular, we document the persistence of large (positive or negative) daily returns. In a multivariate setting , we find that foreign holdings provide a good hedge against changes in domestic volatility after good shocks but a bad hedge after crashes. Finally, using generalized impulse responses, we show that the effect of shocks on the higher moments of the distribution is short-lasting.

KEYWORDS: GARCH model, non-normality, kurtosis, skewness, stock returns, volatility

Both of us acknowledge help from the Swiss National Science Foundation through NCCR FINRISK (Financial Valuation and Risk Management). We benefited from comments and discussions with Tim Bollerslev, Ales Cerny, René Garcia, Eric Jacquier, Nour Meddahi, and Raman Uppal. We are grateful to three referees as well as to the associate editor for their insightful comments. The usual disclaimer applies. A Technical Appendix containing the proofs of our propositions and additional results is available on the webpage "http://www.hec.unil.ch/ejondeau/Publications/Publications.htm."

Received November 6, 2007; revised September 3, 2008; accepted October 16, 2008


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