1. (10 pt each) Consider a non-dividend-paying stock whose current price S(0) = S is $35. After each period, there is a 55% chance that the stock price goes up by 20%. If the stock price does not go up, then it drops by 20%. A European call option and a European put option on this stock expire on the same day in four months at $38 strike. Current risk-free interest rate is 4.8% per annum, compounded monthly. Count a month as one period. (a) Construct a four-period binomial lattice tree to calculate all the possible stock prices from t = 0 to t = 4. (b) Use a four-period binomial lattice tree to calculate the current (t = 0) put option price. (c) Use Put-Call Parity to calculate the call option price. (d) Find the price of an American put option on the stock that has the same strike price and expiration date