Problem 5. (Put-on-call) (7 pts) Consider a 3-step binomial model with S0=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(KpC2E,0), where C2E 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 Kp=12. In summary, this PoC gives the holder the right to sell the underlying call at time 2 with a price equal to Kp. a) (1 pts) Draw the binomial tree of the stock price. b) ( 3pts ) Calculate the value at t=2 of the European call option. (Notice that there are three nodes: S2uu,S2ud,S2dd) c) (3 pts) Find out the initial price of this put-on-call option