STOCHASTIC METHODS IN FINANCE 2021–22 STAT0013
Exercises 2 – Introduction to Derivatives
1. What is the difference between entering into a long forward contract when the forward price is £50 and taking a long position in a call option with a strike price of £50?
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2. You would like to speculate on a rise in the price of a certain stock. The current stock price is £29 and a 3-month call with strike of £30 costs £2.90. You have £5,800 to invest. Identify two alternative strate- gies, one involving an investment in the stock and the other involving investment in the option. What are the potential gains and losses from each?
3. Show that a long forward contract is equivalent to a long position in a European call option and a short position in a European put option with the same strike price.
4. Suppose that you enter into a six-month forward contract on a non- dividend paying stock when the stock price is £30 and the risk-free interest rate (with continuous compounding) is 12% per annum. What is the forward price?
5. An one-year long forward contract on a non-dividend paying stock is entered when the stock price is £40 and the risk-free interest rate (with continuous compounding) is 10% per annum.
(a) What is the forward price? (the initial value of the forward con- tract is of course zero).
(b) Six months later the price of the stock is £45 and the risk-free interest rate is still 10%. What is the price of a new forward written at this time with the same delivery date?
(c) What is the value of the original forward contract at this time?
6. A stock is expected to pay a dividend of $1 per share in two months and again in five months. The stock price is $50 and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. What is the forward price of a six-month forward contract?
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