Exponential-Type GARCH Models With Linear-in-Variance Risk Premium
(2021) Journal of Business and Economic Statistics — Vol. 39, n° 2, p. 589-603 (2021)
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- 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.
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Hafner, C., & Kyriakopoulou, D. (2021). Exponential-Type GARCH Models With Linear-in-Variance Risk Premium. Journal of Business and Economic Statistics, 39(2), 589-603. https://doi.org/10.1080/07350015.2019.1691564 (Original work published 2021)