a. John is considering buying some options. On the 1st of October an out of the money call option written on the stock of company JHG has a strike price of £50, expires in one month and is currently selling for £8. On the same date, another out of the money call option written on JHG’s stock has the same strike price, expires in two months and has a price £9. The stock price of JHG on the 1st of October is £44.
i. John is intending to buy the option that expires in one month, as it is cheaper. Is John’s logic here correct? Explain.
ii. On the same date, a two-month call option with a £50 strike price written on the shares of another company, called OIU, is trading for £10. Discuss why this option is more expensive than the corresponding option for JHG, assuming that on the 1st October the stock price for OIU was also £44.
b. One share in company CALI is currently worth £50. CALI’s shares have been trading in a very narrow range for the previous 3 months, and Marshall believes that this stock will continue trading in this narrow range for the next three months. The price for a 3-month put option on CALI’s shares with a strike price of £50 is currently priced at £4. Answer the following, showing all relevant calculations.
i. If the risk-free rate is 10% per year, what must be the price of a 3-month call option on CALI’s stock with an exercise price of £50?
ii. Describe what option strategy Marshall could use to exploit his beliefs about the future stock price movement, and calculate how far the stock price of CALI would need to move for Marshall’s profits to turn negative.
iii. Use a diagram to illustrate Marshall’s payoffs at the option’s expiration date.
c. Dre purchases a stock for £38 and a put with a strike price of £35 for £0.50. Dre also sells a call with a strike price of £40 for £0.50. Both options expire at the same time. Calculate the payoffs to the strategy, if at the options’ expiration date, the stock price falls below £35, if it is between £35 and £45, or if the stock price exceeds £40. Draw Dre’s profit/loss from this strategy at the options’ expiration date.
d. Snoop wants to buy 50 shares in the company DOGG, which now trades for £350 pounds a share. He believes that each of these shares could be worth either £400 or £300 in one year’s time. How many put options on DOGG with strike price of £350 which mature in one year does Snoop need to buy, so that the value of his portfolio in one year’s time is hedged with respect to movements in the stock price of DOGG? Use your calculations to demonstrate that this is indeed the case in this particular instance, where the stock price could be worth either £400 or £300. Also calculate how much money Snoop should pay for these put options now, assuming that the risk-free rate is 4% per year.