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Exponential-type GARCH models with linear-in-variance risk premium

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  • HAFNER Christian,

    (Université catholique de Louvain)

  • KYRIAKOPOULOU Dimitra,

    (Université catholique de Louvain, CORE, 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, 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.

Suggested Citation

  • HAFNER Christian, & KYRIAKOPOULOU Dimitra,, 2019. "Exponential-type GARCH models with linear-in-variance risk premium," LIDAM Discussion Papers CORE 2019013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2019013
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    More about this item

    Keywords

    GARC H-in-Mean; EGARCH; Log-GARCH; CAPM; risk premium; maximum likelihood; 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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