4. (10 points) An asset with known value So at time t-O and unknown value S r is modeled by S(T) = ezov T+Ins,wr where z is a standard normal random variable is a constant. Then for any payoff function A, the expected value of A(S(T) is a) Let K > 0 be a constant. Solve for x = A such that erwT+lnsowT-K b) A cash-or-nothing call with strike K has payoff (v)- Find EIA(S(T) and express the result in terms of quantities defined on p. 1. 1, > K 10, y K 4. (10 points) An asset with known value So at time t-O and unknown value S r is modeled by S(T) = ezov T+Ins,wr where z is a standard normal random variable is a constant. Then for any payoff function A, the expected value of A(S(T) is a) Let K > 0 be a constant. Solve for x = A such that erwT+lnsowT-K b) A cash-or-nothing call with strike K has payoff (v)- Find EIA(S(T) and express the result in terms of quantities defined on p. 1. 1, > K 10, y K