Consider futures on an underlying asset that pays N discrete dividends between t and T and let D_i denote the amount of the ith dividend paid on the ex-dividend date t_i. Show that the futures price is given by

where S is the current asset price and r is the riskless interest rate. Consider a European call option on the above futures. Show that the governing differential equation for the price of the call, c_F (F, t), is given by (Brenner, Courtadon and Subrahmanyan, 1985)

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F(S, t) = Ser(T-t). N i=1 Die (T-ti),