1. Given the risk-neutral process of a non-tradable market index as, dSt St Y(t)dt + sdzt where y(t) is a time function and o is a constant. Assume also that risk-free interest rate r is constant and flat. (a) Use risk-neutral pricing to determine the futures price Ky of the index with maturity at T. Note : Maturity payoff of a futures contract is defined as FT=ST - K1, where K is the futures delivery price defined at current time. The choice of K is defined in the way that current price of a futures contract is zero for which there is no cost on both sides in entering the agreement. (15 points)