The price of stock ABC is currently $50 and is assumed to follow a two-step binomial tree process. Over each of the next two 3-month periods the price of stock ABC is expected to either increase by 10% or decrease by 10%. The risk-free rate of interest is 10% per year with continuous compounding.

a) Calculate the probabilities that the price of stock ABC goes up and down in the risk neutral world. [2 marks]

b) Use the binomial tree formulas to determine the current price of a 6-month European put option on stock ABC with a strike price $54. [8 marks]

c) Suppose now that the expected return on the ABC stock price is 15%. Determine the current price of the European put in point b). Justify your answer. [5 marks]

d) Use the European put-call parity relationship to determine the current price of a European call option that has the same strike price and time to expiration as the European put option in point b).