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

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Version 2 2019-12-23, 20:13
Version 1 2019-11-14, 14:53
journal contribution
posted on 2019-12-23, 20:13 authored by Christian M. Hafner, Dimitra Kyriakopoulou

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.

Funding

The second author would like to acknowledge financial support from the MOVE-IN Louvain Post-doctoral Fellowship, co-funded by the Marie Curie Actions of the European Commission.

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