(20 points) A down-and-in cash call is a claim that pays $1 at maturity date T provided the barrier B is hit and Sr > K. Denote the price of a down-and-in cash call by DICashCall(S,K,T,B) where is the current (non-dividend paying) stock price, and T is the time to maturity. Suppose B K. Denote the price of a down-and-out cash call by DOCashCall(S, K,T,B) where S is the current (non-dividend paying) stock price, and T is the time to maturity. (a) Prove in-and-out parity DOCashCall(S,K,T, B)= CashCall(S,K,1,B) DICashCall(S, K,T, B). where the cash-call option is defined in Question 1. (b) Find the pricing formula for the down-and-out cash call. Compute numerically the value of DOCashCall(S,K,T,B) for parameters S = 100; K = 90, 95, 100, 105, 110;T = 1; B = 80; r = 5%; 0 = 20%;q=1%.