1. Consider a non-dividend-paying stock whose current price S(0) = S is $40. After each period, there is a 60% chance that the stock price goes up by 20%. If the stock price does not go up, then it drops by 10%. A European call option and a European put option on this stock expire on the same day in 3 months at $43 strike. Current risk-free interest rate is 6% per annum, compounded monthly. Count a month as one period.
(a) Construct a three-period binomial lattice tree to calculate the stock price after three months.
(b) Construct a three-period binomial lattice tree to calculate the current (t = 0) call option price.
(c) Construct a three-period binomial lattice tree to calculate the current (t = 0) put option price.
(d) Use Put-Call Parity to verify your answers from (c) and (d). If there is any error (discrepancy), provide your opinion on what caused the discrepancy.
2. Find the price of an American put option on the stock in problem 1 that has the same strike price and expiration date.