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Title: The tail behaviour due to the risk premium in AR-GARCH-in-mean, GARCH-AR and double-autoregressive-in-mean models Authors:  Christian Dahl - University of Southern Denmark (Denmark)
Emma Iglesias - University of A Coruna (SPAIN) (Spain) [presenting]
Abstract: Results in extreme value theory are extended by describing the tail behaviour when a risk premium component is added in the mean equation of different conditional heteroskedastic processes. We study three types of parametric models that are able to generate a risk premium: the traditional GARCH-M, the double autoregressive model with risk premium and the GARCH-AR model. We find that if an autoregressive process is introduced in the mean equation of a traditional GARCH-M process, the tail behavior is the same as if it is not introduced. However, if we add an autoregressive process to a conditional volatility model with a risk premium component and lags of data in the conditional variance, then the tail behaviour changes. The GARCH-AR model also has a different tail index than the traditional AR-GARCH model. In our simulations, we show that the larger tail indexes are generated when using the traditional GARCH-M model. Also, when the risk premium increases, the tail index tends to fall with the only exception of specifying a risk premium with the logarithm of the volatility in the double autoregressive model. We also show some parameter settings where the strong stationarity condition of the risk premium models fails.