Deck 15: Options on Stock Indices and Currencies

Question 1

To create a range forward contract in order to hedge foreign currency that will be received, a company should: choose one)

A) Buy a put and sell a call on the currency with the strike price of the put higher than that of the call
B) Buy a put and sell a call on the currency with the strike price of the put lower than that of the call
C) Buy a call and sell a put on the currency with the strike price of the put higher than that of the call
D) Buy a call and sell a put on the currency with the strike price of the put lower than that of the call

Answer 1

B

Question 2

The put-call parity formula for options on a stock paying known dividend yields is the same as that for options on a non-dividend-paying stock, except that:

A) S₀ is replaced by S₀e^qT
B) S₀ is replaced by S₀e^rT
C) S₀ is replaced by S₀e^−qT
D) S₀ is replaced by S₀e^−rT

Answer 2

C

Question 3

A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months, and would like to use options on the S&P/ASX 200 to provide protection against the portfolio falling below $9.5 million. The S&P/ASX 200 is currently standing at 5000 and each contract is on 10 times the index.
i) If the portfolio has a beta of 1, how many put option contracts should be purchased? _ _ _ _ _ _
ii) If the portfolio has a beta of 1, what should the strike price of the put options be? _ _ _ _ _ _
iii) If the portfolio has a beta of 0.5, how many put options should be purchased? _ _ _ _ _ _
iv) When the portfolio has a beta of 0.5, what should the strike prices of the put options be if the insured level of $9.5 million were to include dividends? Assume that the risk-free rate is 10% per annum and the dividend yield on both the portfolio and the index is 2% per annum. _ _ _ _ _ _

Answer 3

i): 200 ii): 4750 iii): 100 iv): 4200

Question 4

Consider a European put option on an index. The index level is 1000, the strike price is 1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum. What is a lower bound to the option price? Give two decimal places.) _ _ _ _ _ _

Question 5

To create a range forward contract in order to hedge foreign currency that will be paid, a company should: choose one)

A) Buy a put and sell a call on the currency with the strike price of the put higher than that of the call
B) Buy a put and sell a call on the currency with the strike price of the put lower than that of the call
C) Buy a call and sell a put on the currency with the strike price of the put higher than that of the call
D) Buy a call and sell a put on the currency with the strike price of the put lower than that of the call

Question 6

Suppose that the current Australian dollar/US dollar exchange rate is 1.08. The risk-free rates of interest in Australia and the US are 2.75% and 1.24% per annum continuously compounded) respectively. A European put option to sell one US dollar for AUD1.08 in six months costs $4.20. What is the price of a six-month call option to buy AUD1.08 with one US dollar? _ _ _ _ _ _ _

Question 7

Options on an exchange rate can be valued using the formula for an option of a stock paying a continuous dividend yield where the dividend yield is replaced by: choose one)

A) The domestic risk-free rate
B) The foreign risk-free rate
C) The foreign risk-free rate minus the domestic risk-free rate
D) None of the above

Question 8

Consider a European call option on a currency. The exchange rate is 1.0000, the strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. What is a lower bound to the option price? Give four decimal places.) _ _ _ _ _ _