Consider the pricing of a put option on AAPL. The spot price is $140, the strike price is $140, and the maturity is six months. The growth rate of the AAPL is 2% and its annual volatility is 30%. The annualized interest rate for monthly compounding is fixed at 0.2%.

3.1. (4) Calculate the option value and hedge ratio (i.e., alpha) using a six-step binomial tree. 3.2. (4) If the path of the stock price for the next six months is {(0,0), (0,1), (1,2), (2,3), (3,4), (3,5), (4,6)}, provide the alphas for delta hedging along the path.