Phillip wants to price a 6-month European put option with a strike price of $33 on a share in Planet Express Corporation (PEX). The current price for a PEX share is $31. Phillip has used past data and his own judgement to estimate the volatility of these shares to be 18% per annum. The risk-free continuously compounding interest rate is 2% per year.

a) Construct a 3-step binomial tree showing the possible share prices over the next 6 months. Also, clearly show the corresponding probabilities for an upward and a downward movement in the share price. [4 marks]

b) Using your binomial tree from part a) and the information given above, calculate the corresponding 3-step binomial tree for the option, and clearly state the fair price of the option according to the given information. [3 marks]

c) Phillip wants to also calculate the price of a 6-month European call option on PEX shares with a strike price of $28. Should the price of this call option and the price of the put option in b) satisfy the put-call parity? Explain why or why not. [3 marks]