Grace is an investment banker who has had an excellent year at work, and has been told she will receive a significant cash bonus at the end of the year. She plans to use the money to buy shares in Fortescue Metals Group, as she is passionate about supporting renewable green energy initiatives. However, she is concerned that the share price of Fortescue will rise between now and the end of the year, and therefore she wishes to buy call options on Fortescue stock.

Unfortunately, there are no call options currently available. However futures on Fortescue Ltd are priced at $15.50 and put options on Fortescue struck at $15.50 are trading at $0.52. Both the futures and the put options expire on 31 December 2021, the day Grace will receive her bonus.

Grace therefore wishes to combine a position in the futures and a position in the put option such that she can replicate the profit from purchasing a call option on the company. Given this information:

a) Describe how Grace could form a portfolio consisting of Fortescue futures and put options that will replicate the profit from purchasing Fortescue call options.

b) Draw diagrams depicting the following (note: in drawing these diagrams you should have profit on the vertical axis and the spot price at expiry on the horizontal axis):

i. The profit from the futures position described in part (a) as a function of the spot price at expiry

ii. The profit from the put option position described in part (a) as a function of the spot price at expiry

iii. The overall profit from your portfolio described in part (a) as a function of the spot price at expiry

c) Imagine that Fortescue call options have just become available. If European put options on Fortescue struck at $15.50 and with two months to maturity are trading at $0.52, European call options on Fortescue struck at $15.50 and with two months to maturity are trading at $0.66, the risk free rate is 2.5% and you could currently buy shares in Fortescue in the spot market for $18, is there an arbitrage opportunity in this market based on put-call parity? If so, describe the strategy and construct a table using the specific numbers in this question to illustrate that the riskless profit is locked in whether the stock price is $10 or $20.