Exercise . Consider an asset paying a dividend of DT at time T and no other dividends. You want to price the asset at time t < T. Assume that DT = Et[DT]eX for a normally distributed random variable X ∼ N(− 

 σ 

X, σ 

X), so that E[eX] = .

Also assume that the state-price deflator satisfies ζT = ζteY, where X and Y are jointly normally distributed with correlation ρ and Y ∼ N(μY, σ 

Y). Show that the time t price of the asset is Pt = Et[DT] exp *

μY +





σ 

Y + ρσXσY

.