Consider a non-dividend-paying stock whose current price S(0) is $60. After each period, there is a 50% chance that the stock price goes up by 25%. If the stock price does not go up, then it drops by 20%. A European call option, a European put option, and an American put option on this stock expire on the same day in 3 months at $65 strike. Current risk-free interest rate is 9% per annum, compounded monthly. Count a month as one period.

a. Construct a three-period binomial lattice tree and calculate the stock price after three months

b. Using binomial lattice tree calculate the current (t=0) European put option price

c. Use Put-Call Parity to calculate the current call option price d. (20 pt) Find the price of the American put option at time 0