Assuming current stock price of ABC Company is $100. Over each of the next two six-month periods, the price is expected to go up by 10% or down by 10% during each six-month period. The risk-free interest rate is 8% per annum with annual compounding.

Required:

a. Calculate the option premium for a one-year European call option with an exercise price of $80. Show your calculation steps. (8 marks)

b. Using the option premium calculated in Part a and the information provided in this question, estimate the premium of a one-year European put option that has the same strike price and the same expiration date. (4 marks)