A stock price is currently $80. Over each of the next two six-month periods, it is expected to go up by 6% or down by 6%. The risk-free interest rate is 5% per year with semi-annual compounding.

Part I.

Use the two-steps binomial tree model to calculate the value of a one-year American put option with an exercise price of $80.

Part II.

Is there any early exercise premium contained in price of the above American put option? If there is, what is the early exercise premium?

Part III.

Discuss how you can hedge risk if you write the above put option with an exercise price of $80 and 1-year maturity.