rugarch fitting Duan's 1995 model

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rugarch fitting Duan's 1995 model

Argyrios Ramandanis

I am trying to fit, using rugarch library, the Duan's 1995 model for stock
option pricing.

Duan's model includes the mean , garch in mean, their special GARCH
specification and finally one more factor, which is 0.5* variance. More
specifically it is:

rt = r + λ*sigma - 0.5 * variance + et*sigma

My problem is that I cannot find how I can include the -0.5*variance in the
mean model. λ*sigma I can use the archm function but not this extra item.

Do you know how I can force ugarchspec to add this? Also in general, how
can I add extra endogenous variables other than the standard ones?

One more question, the GARCH model of Duan's paper looks like the
family-GARCH model where λ=δ=2, but the family-GARCH is using standardized
residuals where Duan is using the raw residuals. Can this be changed as

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