Kozhan et al. (2011) show skew risk premium is related to variance risk premium in a general

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Kozhan et al. (2011) show skew risk premium is related to variance risk premium in a general equilibrium model.

(a) Compare and contrast the Epstein-Zin utility in Kozhan et al. (2011, Section 6.1) with HARA utility.

(b) Show how the \(P\) and \(Q\) dynamics of S\&P 500 are connected through this Epstein-Zin utility function.

(c) What is the consequence if you replace the Epstein-Zin utility with Merton's power utility which is in the HARA family.

(d) What is the relationship between variance risk premium and skewness risk premium? What are their relationships with jumps? (Kozhan et al. 2011)

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