Suppose you are an option trader and are now considering the options on the shares of HSBC.

The current stock price of HSBC is $60. It is expected that the stock price of HSBC will go up by 12% or down by 12% over each of the next two three-month periods. The risk-free interest rate is 3% per annum with continuous compounding.

Required

a Determine the value of a six-month European call option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. (12 marks)

b Determine the value of a six-month European put option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. (6 marks)

c Determine the value of a six-month American put option on the shares of HSBC with a strike price of $65 using a binomial option pricing model. Explain whether the American put option should be exercised at the end of the first three-month period. (12 marks)