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Contemporaneous Asymmetry in Weak GARCH Processes

Author

Listed:
  • EL BABSIRI, Mohamed

    (Caisse des Dépôts et Consignations, Paris, France)

  • ZAKOIAN, Jean-Michel

    (CREST-INSEE, Université de Lille I, France)

Abstract

The paper proposes an original class of conditionally heteroskedastic models aimed to capture a new concept of asymmetry. Not only past up and down moves of stock market returns have different impacts on the conditional variance, but also, positive and negative changes are governed by different (asymmetric) volatilities. We give a formal content to asymmetry in a weak GARCH framework. The probabilistic structure of the proposed class of models is analyzed in details: constraints sullicient to guarantee the covariance stationarity and existence of white noise solutions are developed; necessary and sufficient conditions for strict stationarity are presented. The paper also provides theoretical results on the quasi-maximum likelihood estimation in a context where the usual martingale difference assumption is ruled out. Finally, it is shown that the asymmetric hypotheses underlying the model are strongly supported by stock returns data, through an empirical analysis on the French stock market.

Suggested Citation

  • EL BABSIRI, Mohamed & ZAKOIAN, Jean-Michel, 1996. "Contemporaneous Asymmetry in Weak GARCH Processes," LIDAM Discussion Papers CORE 1996004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1996004
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1996.html
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    Cited by:

    1. Christian M. Hafner & Wolfgang HÄrdle, 2000. "Discrete time option pricing with flexible volatility estimation," Finance and Stochastics, Springer, vol. 4(2), pages 189-207.

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