Consider the put-call parity relationships.

a) Write down the formulation of the put-call parity relationship for European options on a non-dividend paying stock and comment on its importance within options theory. [5 marks]

b) Consider the prices of a European put option and a European call option on the same stock ABB. The current price of stock ABB is $20.The time to expiration of both put and call options is 2 years, and both options have an exercise price of $35. The risk-free interest rate is 6% per year with continuous compounding, and the current price of the put option is $2.5. Calculate the current price of the call option. [8 marks]

c) Explain the differences between the European put-call parity and American put-call parity relationships. [7 marks]