Consider a non-dividend-paying stock whose current price S(0) = S 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 and a European put option on this stock expire on the same day in 4 months at $65 strike. Current risk-free interest rate is 4.8% per annum, compounded monthly. Count a month as one period. PLEASE SHOW FORMULAS USED

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.