The price of a share is currently $60. During each of the next two six-month periods, it is expected to increase 6% or decrease 6%. The risk-free interest rate is 5% per year with semi-annual compounding.

Part I. Use the two-step binomial tree model to calculate the value of a one-year European put option with a strike price of $61. 

Part II. Consider how you can hedge the risk when you initially write the put option. (4 points)

Part III. Assume that six months have passed, discuss how you can hedge the risk when you realize that the stock price is $63.6.