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

Christian Hafner and Dimitra Kyriakopoulou

Journal of Business & Economic Statistics, 2021, vol. 39, issue 2, 589-603

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.

Date: 2021
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Working Paper: Exponential-Type GARCH Models With Linear-in-Variance Risk Premium (2020)
Working Paper: Exponential-type GARCH models with linear-in-variance risk premium (2019)
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DOI: 10.1080/07350015.2019.1691564

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