1. Given the risk-neutral process of a non-tradable market index as, ds = y(t)dt + odz S, where y(t) is a time function and o is a constant. Assume also that risk-free interest rate r is constant and flat. (b) Consider a cash-or-nothing digital option written on the market index with strike price L and maturity at time T. The maturity payoff of this option is given by NIS-, 7)={; if St> 0, if SSL Suppose the risk-neutral drift y(t) is not known. Use futures price defined in (a) to calibrate the market index at option's maturity under risk-neutral preference, and show that the current price of the digital option is given by fore-TPN log('83) OVT Evaluate also the forward price of the digital option f(s, t) conditional to a given market index S, at time t during the life of the option. 1. Given the risk-neutral process of a non-tradable market index as, ds = y(t)dt + odz S, where y(t) is a time function and o is a constant. Assume also that risk-free interest rate r is constant and flat. (b) Consider a cash-or-nothing digital option written on the market index with strike price L and maturity at time T. The maturity payoff of this option is given by NIS-, 7)={; if St> 0, if SSL Suppose the risk-neutral drift y(t) is not known. Use futures price defined in (a) to calibrate the market index at option's maturity under risk-neutral preference, and show that the current price of the digital option is given by fore-TPN log('83) OVT Evaluate also the forward price of the digital option f(s, t) conditional to a given market index S, at time t during the life of the option