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