10. Asymmetries

  1. Christian Francq1 and
  2. Jean-Michel Zakoïan1,2

Published Online: 14 JUL 2010

DOI: 10.1002/9780470670057.ch10

GARCH Models: Structure, Statistical Inference and Financial Applications

GARCH Models: Structure, Statistical Inference and Financial Applications

How to Cite

Francq, C. and Zakoïan, J.-M. (2010) Asymmetries, in GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470670057.ch10

Author Information

  1. 1

    University Lille 3, Lille, France

  2. 2

    CREST, Paris, France

Publication History

  1. Published Online: 14 JUL 2010
  2. Published Print: 23 JUL 2010

ISBN Information

Print ISBN: 9780470683910

Online ISBN: 9780470670057



  • asymmetry property;
  • Log-GARCH;
  • quadratic GARCH model (QGARCH);
  • qualitative threshold ARCH (QTARCH)model;
  • threshold GARCH (TGARCH) model


The absence of significant autocorrelations of the returns and the correlation of their modulus or squares constitutes the basic properties motivating the introduction of GARCH models. But just as evident is the existence of an asymmetry in the impact of past innovations on the current volatility. This chapter discusses GARCH models that allow asymmetry property to be incorporated. A natural way to introduce asymmetry is to specify the conditional variance as a function of the positive and negative parts of the past innovations. The threshold GARCH (TGARCH) class of models introduces a threshold effect into the volatility. The following class is very general and contains the standard GARCH, the TGARCH, and the Log-GARCH. Among other asymmetric GARCH models, the chapter discusses the qualitative threshold ARCH (QTARCH) model, and the quadratic GARCH model (QGARCH or GQARCH).

Controlled Vocabulary Terms

generalized autoregressive conditional heteroskedasticity; nonlinear asymmetric generalized autoregressive conditional heteroskedasticity