Deck 15: Options on Stock Indices and Currencies

Question 1

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 an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 0.5? 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.

A) 400
B) 410
C) 420
D) 430

Answer 1

D

Question 2

Suppose that the domestic risk free rate is r and dividend yield on an index is q. How should the put-call parity formula for options on a non-dividend-paying stock be changed to provide a put-call parity formula for options on a stock index? Assume the options last T years.

A) The stock price is replaced by the value of the index multiplied by exp(qT)
B) The stock price is replaced by the value of the index multiplied by exp(rT)
C) The stock price is replaced by the value of the index multiplied by exp(-qT)
D) The stock price is replaced by the value of the index multiplied by exp(-rT)

Answer 2

C

Question 3

For 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. How low can the option price be without there being an arbitrage opportunity?

A) 0.1048
B) 0.0900
C) 0.1344
D) 0.1211

Answer 3

A

Question 4

A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option?

A) 0.98N(0.25)-1.11(0.05)
B) 0.98N(-0.3)-1.11N(-0.5)
C) 0.98N(-0.5)-1.11N(-0.7)
D) 0.98N(0.10)-1.11N(0.06)

Question 5

Which of the following is true when a European currency option is valued using forward exchange rates?

A) It is not necessary to know the domestic interest rate or the spot exchange rate
B) It is not necessary to know either the foreign or domestic interest rate
C) It is necessary to know the difference between the foreign and domestic interest rates but not the rates themselves
D) It is not necessary to know the foreign interest rate or the spot exchange rate

Question 6

Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be paid?

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 7

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 an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What position is required if the portfolio has a beta of 0.5?

A) Short 200 contracts
B) Long 200 contracts
C) Short 100 contracts
D) Long 100 contracts

Question 8

The domestic risk-free rate is 3%. The foreign risk-free rate is 5%. What is the risk-neutral growth rate of the exchange rate?

A) +2%
B) -2%
C) +5%
D) +3%

Question 9

A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement?

A) 0.4704
B) 0.5065
C) 0.5592
D) 0.5833

Question 10

Index put options are used to provide protection against the value of the portfolio falling below a certain level. Which of the following is true as the beta of the portfolio increases?

A) The cost of hedging increases
B) The options require a lower strike price
C) The number of options required increases
D) All of the above

Question 11

A portfolio manager in charge of a portfolio worth $10 million is concerned that stock prices might decline rapidly during the next six months and would like to use options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What position is required if the portfolio has a beta of 1?

A) Short 200 contracts
B) Long 200 contracts
C) Short 100 contracts
D) Long 100 contracts

Question 12

For a European put option on an index, the index level is 1,000, 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. How low can the option price be without there being an arbitrage opportunity?

A) $50.00
B) $43.11
C) $29.21
D) $39.16

Question 13

What should the continuous dividend yield be replaced by when options on an exchange rate are valued using the formula for an option of a stock paying a continuous dividend yield?

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 14

Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be received?

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 15

A binomial tree with three-month time steps is used to value a currency option. The domestic and foreign risk-free rates are 4% and 6% respectively. The volatility of the exchange rate is 12%. What is the probability of an up movement?

A) 0.4435
B) 0.5267
C) 0.5565
D) 0.5771

Question 16

A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option?

A) 1.11N(0.7)-0.98N(0.5)
B) 1.11N(-0.7)-0.98N(-0.5)
C) 1.11N(0.7)-0.98N(0.4)
D) 1.11N(-0.06)-0.98N(-0.10)

Question 17

What is the size of one option contract on the S&P 500?

A) 250 times the index
B) 100 times the index
C) 50 times the index
D) 25 times the index

Question 18

What is the same as 100 call options to buy one unit of currency A with currency B at a strike price of 1.25?

A) 100 call options to buy one unit of currency B with currency A at a strike price of 0.8
B) 125 call options to buy one unit of currency B with currency A at a strike price of 0.8
C) 100 put options to sell one unit of currency B for currency A at a strike price of 0.8
D) 125 put options to sell one unit of currency B for currency A at a strike price of 0.8

Question 19

Which of the following is NOT true about a range forward contract?

A) It ensures that the exchange rate for a future transaction will lie between two values
B) It can be structured so that it costs nothing to set up
C) It is constructed from two options and a forward contract
D) It can be used to hedge either a future inflow or a future outflow of a foreign currency

Question 20

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 an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 1?

A) 425
B) 450
C) 475
D) 500