Question 7 (Total 14 marks)

The stock price of Commonwealth Bank of Australia (CBA) is currently $80. Over each of the next two six-month periods, it is expected to go up by 10% or down by 10%. The dividend yield of this stock is 4% annum. The risk-free interest rate is 12% per annum with continuous compounding.

Required:

a. What are the probabilities of stock price up and down respectively? Show your calculation. (3 marks)

b. Draw a binomial tree of European call option on this stock with a strike price of $84, label stock price, option value (payoff) and hedge ratio at each step/node of the tree. Show your calculation of the call option current value and hedge ratio. (6 marks)

c. Draw a binomial tree of American put option on this stock with a strike price of $84, label stock price, option value (payoff) and hedge ratio at each step/node of the tree. Show your calculation of the put option current value and hedge ratio. (5 marks)