Mr. and Mrs. Jones both wish to buy stocks in Widgets Inc. They don't have enough money right now, so they are considering buying either forwards or options on the stocks, both with a term of 4 years. The stock price at time 0 is 10 with standard deviation of 12% per annum. The stock does not pay any dividend. The continuously compounded risk-free rate of interest is 5% per annum.

i.Calculate the 4-year forward price on one stock. [2 marks]

ii.Calculate the price at time 0 of a 4-year call option on one stock with a strike price of 12.21. [5 marks]

Mrs. Jones enters into one forward contract, while Mr. Jones buys one call option. At time 4 the stock is worth 12.

iii.Calculate the accumulated profit or loss at time 4 for Mrs. Jones. [2 mark]

iv.Calculate the accumulated profit or loss at time 4 for Mr. Jones. [3 marks]

v.Explain why Mr. Jones makes a loss despite having an option that does not force him to buy the stock. [4 marks]

vi.Calculate the range of stock prices at time 4 which would leave Mr. Jones better off than Mrs. Jones. [4 marks]