A stock price is currently $50. A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. Use two-period binomial models to value the six-month options on this stock. Remember to show detailed calculations of the option value at each node.

• What is the value of a six-month European call option with a strike price of $51?

(3 marks)

• What is the value of a six-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put–call parity.

(3 marks)

• If the put option in part (b) of this question were American, would it ever be optimal to exercise it early at any of the nodes on the tree?

(4 marks)