Exponential-type GARCH models with linear-in-variance risk premium
(2019) , 51 pages
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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, estimation theory of classical GARCH-in-mean models with linear-in-variance risk premium requires strong assumptions and is complete. 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.
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Citations
Hafner, C., & Kyriakopoulou, D. (2019). Exponential-type GARCH models with linear-in-variance risk premium (CORE Discussion Papers 2019/13). https://hdl.handle.net/2078.5/126476