Consider a non-dividend-paying stock whose current price S(0) = S is $50. After each period, there is a 50% chance that the stock price goes up by 15%. If the stock price does not go up, then it drops by 15%. A European call option and a European put option on this stock expire on the same day in 4 months at $55 strike. Current risk-free interest rate is 3.6% per annum, compounded monthly. Count a month as one period. (a) Construct a four-period binomial lattice tree to calculate the stock price after four months. (b) Construct a four-period binomial lattice tree to calculate the current (t = 0) call option price. (c) Construct a four-period binomial lattice tree to calculate the current (t = 0) put option price. (d) Find the price of an American put option on the stock that has the same strike price and expiration date as the European ones.