Problem 4. (Put-on-call) (7 pts) Consider a 3-step binomial model with So = 50, U = 0.2, D = -0.2, and R = 0.05, and a European call option written on this stock with strike price K = 40 and expiry time t = 3. Now, we consider a Put-on-Call (PoC) option written on this European call option, however, with expiry time t = 2, i.e, the final payoff (at t = 2) of PoC option is given by H2 = max (K, -CF, 0), where CE is the value (price) of the underlying European call option at the step t = 2. Assume that the strike price of the outside put option is K, = 12. a) (1 pts) Draw the binomial tree of the stock price. b) (3 pts) Calculate the value at t = 2 of the European call option. (Notice that there are three nodes: Syu, Syd, Sad) c) (3 pts) Find out the initial price of this put-on-call option. Problem 4. (Put-on-call) (7 pts) Consider a 3-step binomial model with So = 50, U = 0.2, D = -0.2, and R = 0.05, and a European call option written on this stock with strike price K = 40 and expiry time t = 3. Now, we consider a Put-on-Call (PoC) option written on this European call option, however, with expiry time t = 2, i.e, the final payoff (at t = 2) of PoC option is given by H2 = max (K, -CF, 0), where CE is the value (price) of the underlying European call option at the step t = 2. Assume that the strike price of the outside put option is K, = 12. a) (1 pts) Draw the binomial tree of the stock price. b) (3 pts) Calculate the value at t = 2 of the European call option. (Notice that there are three nodes: Syu, Syd, Sad) c) (3 pts) Find out the initial price of this put-on-call option