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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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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2019.html
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    1. F Blasques & P Gorgi & S Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models," Papers 1610.02863, arXiv.org.
    2. Hafner, Christian M. & Linton, Oliver, 2017. "An Almost Closed Form Estimator For The Egarch Model," Econometric Theory, Cambridge University Press, vol. 33(4), pages 1013-1038, August.
    3. St. Pierre, Eileen F., 1998. "Estimating EGARCH-M models: Science or art?," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(2), pages 167-180.
    4. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, January.
    5. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, January.
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    Cited by:

    1. Antonis Demos, 2023. "Estimation of Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2309, Athens University of Economics and Business.
    2. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.

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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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