4. (40 points) Consider an option with a being a non-negative parameter and the option pays ((S(T)) - K)+ at maturity date T. Let Ca(S(0), 0,r) be the risk neutral price of the option (with interest rate r and volatility o) when the initial price is S(0). Obviously, C(S(0), o,r) = C(S(0), o, r) is the price of an ordinary call option. Show that, Ca(S(0), o, r) = e(a-1)(r+ao/2)TC((S(0))", ao, ra), where ra = a(r - 0/2) + a0/2. 4. (40 points) Consider an option with a being a non-negative parameter and the option pays ((S(T)) - K)+ at maturity date T. Let Ca(S(0), 0,r) be the risk neutral price of the option (with interest rate r and volatility o) when the initial price is S(0). Obviously, C(S(0), o,r) = C(S(0), o, r) is the price of an ordinary call option. Show that, Ca(S(0), o, r) = e(a-1)(r+ao/2)TC((S(0))", ao, ra), where ra = a(r - 0/2) + a0/2