a) Illustrate the payoffs from a Bear Put Spread by combing a put with exercise price X1 and a put with exercise price X2, where X1 < X2. Exclude the price of the options in your graph of the payoffs. Under which circumstances is this strategy advisable?
b) A stock price is currently £20. It is known that at the end of one month it will be either £22 or £18. The risk-free rate is 3% p.a. with continuous compounding. Use the riskless portfolio method to find the value of a one-month European call option with strike price of £19.
c) Differentiate between the following types of options: European, American, Asian and Bermudan.
d) A four-month European call option on a stock that pays dividends of 80 p in two months is currently selling for ?4. The stock price is ?60 and the strike price is ?58. The risk-free rate of interest is 6% p.a. for all maturities. What opportunities, if any, are there for an arbitrageur? Demonstrate all your steps. Assume continuous compounding throughout.