## 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.

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.

Originalsprog | Engelsk |
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Status | Afsendt - 12. jan. 2018 |