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

Christian Hafner and Dimitra Kyriakopoulou ()
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Dimitra Kyriakopoulou: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2020029, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: EGARCH; GARCH-in-mean; Log-GARCH; Maximum likelihood; Risk premium; Stochastic recurrence equation (search for similar items in EconPapers)
Date: 2020-01-01
Note: In: Journal of Business & Economic Statistics - Vol. To appear
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Related works:
Journal Article: Exponential-Type GARCH Models With Linear-in-Variance Risk Premium (2021)
Working Paper: Exponential-type GARCH models with linear-in-variance risk premium (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020029

DOI: 10.1080/07350015.2019.1691564

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