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Exponential-Type GARCH Models With Linear-in-Variance Risk Premium

Author

Listed:
  • Hafner, Christian

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Kyriakopoulou, Dimitra

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

One of the implications of the intertemporal capital asset pricing model (CAPM) is that the risk premium of the market portfolio is a linear function of its variance. Yet, esti- mation theory of classical GARCH-in-mean models with linear-in-variance risk premium requires strong assumptions and is incomplete. We show that exponential-type GARCH models such as EGARCH or Log-GARCH are more natural in dealing with linear-in- variance risk premia. For the popular and more di¢ cult case of EGARCH-in-mean, we derive conditions for the existence of a unique stationary and ergodic solution and in- vertibility following a stochastic recurrence equation approach. We then show consistency and asymptotic normality of the quasi maximum likelihood estimator under weak moment assumptions. An empirical application estimates the dynamic risk premia of a variety of stock indices using both EGARCH-M and Log-GARCH-M models.

Suggested Citation

  • Hafner, Christian & Kyriakopoulou, Dimitra, 2020. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," LIDAM Reprints ISBA 2020029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2020029
    DOI: https://doi.org/10.1080/07350015.2019.1691564
    Note: In: Journal of Business & Economic Statistics - Vol. To appear
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    More about this item

    Keywords

    EGARCH; GARCH-in-mean; Log-GARCH; Maximum likelihood; Risk premium; Stochastic recurrence equation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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