[15points] Question 2 [default, 016b] Consider a one-period arbitrage-free model (B, S) of market composed of a bank account B with interest rate r, and one underlying S. Answer the following questions. February 21, 2021 1/2 Option Pricing 2020 (a) [5 points] Write down a formula for the function f s.t. f(S, m) is the payoff of the derivative which, at maturity T = 1, gives its buyer a call option with strike K on the underlying S, plus the amount m = R if the call with strike K is in the money (i.e. if ST K). (b) [5 points] From now on let (B, S) be given by the binomial model with K = 12. r = 0, So = 12, S(H) = 20, S(T) = 4, Compute the initial value X(m) of the derivative with payoff X(m) := f(S, m). (c) [5 points] In the above binomial model (B, S), compute the price Mo of the money-back call option, which at maturity T = 1 gives its buyer a call option on S with strike K 12, plus it repays the initial cost Mo if the call with strike K finished in the money. =