John Hull, Fundamentals of Futures and Option Markets - Chap 5
CHAPTER 5 Determination of Forward and Futures Prices
Practice Questions
Problem 5.8. Is the futures price of a stock index greater than or less than the expected future value of the index? Explain your answer. The futures price of a stock index is always less than the expected future value of the index. This follows from Section 5.14 and the fact that the index has positive systematic risk. For an alternative argument, let µ be the expected return required by investors on the index so that E ( ST ) = S0 e ( µ − q )T . Because µ > r and F0 = S0 e( r − q )T , it follows that E (ST ) > F0 . Problem 5.9. A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding. a) What are the forward price and the initial value of the forward contract? b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract? a) The forward price, F0 , is given by equation (5.1) as:
F0 = 40e0.1×1 = 44.21 or $44.21. The initial value of the forward contract is zero.
b) The delivery price K in the contract is $44.21. The value of the contract, f , after six months is given by equation (5.5) as: f = 45 − 44.21e−0.1×0.5
= 2.95 i.e., it is $2.95. The forward price is: 45e0.1×0.5 = 47.31 or $47.31.
Problem 5.10. The risk-free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the six-month futures price? Using equation (5.3) the six month futures price is 150e(0.07−0.032)×0.5 = 152.88 or $152.88.
Problem 5.11. Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November, dividends are paid at a rate of 5% per
Practice Questions
Problem 5.8. Is the futures price of a stock index greater than or less than the expected future value of the index? Explain your answer. The futures price of a stock index is always less than the expected future value of the index. This follows from Section 5.14 and the fact that the index has positive systematic risk. For an alternative argument, let µ be the expected return required by investors on the index so that E ( ST ) = S0 e ( µ − q )T . Because µ > r and F0 = S0 e( r − q )T , it follows that E (ST ) > F0 . Problem 5.9. A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding. a) What are the forward price and the initial value of the forward contract? b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract? a) The forward price, F0 , is given by equation (5.1) as:
F0 = 40e0.1×1 = 44.21 or $44.21. The initial value of the forward contract is zero.
b) The delivery price K in the contract is $44.21. The value of the contract, f , after six months is given by equation (5.5) as: f = 45 − 44.21e−0.1×0.5
= 2.95 i.e., it is $2.95. The forward price is: 45e0.1×0.5 = 47.31 or $47.31.
Problem 5.10. The risk-free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the six-month futures price? Using equation (5.3) the six month futures price is 150e(0.07−0.032)×0.5 = 152.88 or $152.88.
Problem 5.11. Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November, dividends are paid at a rate of 5% per