The Tail Behaviour due to the Presence of the Risk Premium in AR-GARCH-in-Mean, GARCH-AR and Double-Autoregressive-in-Mean Models

Christian M. Dahl, Emma M. Iglesias

Publikation: Working paperForskningpeer review

Abstrakt

We extend the results in Borkovec (2000), Basrak, David and Mikosch (2002a),
Lange (2011) and Franq and Zakoian (2015) 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: 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
a risk premium component to the double autoregressive model, then the tail
behaviour changes with respect to the GARCH-M. 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.
OriginalsprogEngelsk
StatusAfsendt - 12. jan. 2018

Fingeraftryk

Dyk ned i forskningsemnerne om 'The Tail Behaviour due to the Presence of the Risk Premium in AR-GARCH-in-Mean, GARCH-AR and Double-Autoregressive-in-Mean Models'. Sammen danner de et unikt fingeraftryk.

Citationsformater