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

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  • Christian M. Hafner
  • Dimitra Kyriakopoulou

Abstract

One of the implications of the intertemporal capital asset pricing model is that the risk premium of the market portfolio is a linear function of its variance. Yet, estimation 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 difficult case of EGARCH-in-mean, we derive conditions for the existence of a unique stationary and ergodic solution and invertibility 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. Supplementary materials for this article are available online.

Suggested Citation

  • Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    • Handle: RePEc:taf:jnlbes:v:39:y:2021:i:2:p:589-603
    DOI: 10.1080/07350015.2019.1691564
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    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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