-V2Y; Question 5. (10 points) Consider a standard Black-Scholes market where the stock price S(T) has a log-normal distribution. In other words, under the risk-neutral measure, S(T) has a representation S(T) = S(O)(n-102)T to vz where, Z is a standard normal random variable, r > O is the continuously compounded interest rate, and o > 0 is the volatility of the stock. Also, let o be the C.D.F. of the standard normal distribution: 0(3) = . (a) (3 points) Let l{s(T)>K} denote a random variable that takes the value 1 if S(T) > K and the value 0 if S(T) SK. Find an expression for E*1 1{s(T)>K}, the risk-neutral expectation of l{s(T)>K}. For parts (b) and (c) below, consider a pay-later call option. This is a standard European call option with strike price $K and maturity T, with the difference that the premium $p for purchasing the option is paid at T and only if the option has positive value at maturity. In other words, the buyer pays nothing to the seller at t=0. The buyer pays a fixed amount $p to the seller at time T if S(T) > K. If S(T) O is the continuously compounded interest rate, and o > 0 is the volatility of the stock. Also, let o be the C.D.F. of the standard normal distribution: 0(3) = . (a) (3 points) Let l{s(T)>K} denote a random variable that takes the value 1 if S(T) > K and the value 0 if S(T) SK. Find an expression for E*1 1{s(T)>K}, the risk-neutral expectation of l{s(T)>K}. For parts (b) and (c) below, consider a pay-later call option. This is a standard European call option with strike price $K and maturity T, with the difference that the premium $p for purchasing the option is paid at T and only if the option has positive value at maturity. In other words, the buyer pays nothing to the seller at t=0. The buyer pays a fixed amount $p to the seller at time T if S(T) > K. If S(T)