Assignment:
Multiple Choice
Each question in this part is worth 2.5 points. Circle the correct answer.
Q 1. Put-Call parity for European options on stock index under BSM model can be used to:
a. show how far in-the-money put options can get.
b. find how far in-the-money call options can get.
c. show the precise relationship between put and call prices given unequal exercise prices and equal expiration dates.
d. that the value of a call option is always twice that of a put given equal exercise prices and equal expiration dates.
e. find the value of a put option if the price a call option with the same T and K as for put is given from BSM model.
Q 2. Which statement is correct about the estimation of European currency option and stock index option prices?
a. We cannot use the Black-Scholes-Merton (BSM) model to estimate the currency option prices.
b. We can use the BSM model to estimate stock index option prices after accounting for dividend yield but cannot use it to price currency options even after variable adjustments.
c. We can use the BSM model to estimate the prices of currency options and stock index options after renaming the variables in the BSM model such as the stock price and dividend rate with their counterparts under the currency and stock index situations.
d. We cannot use BSM model to price currency, stock index options, and futures options under any scenario about dividend payments and foreign risk-free interest rate.
e. Both b and c are correct.
Q 3. Which are the reasons for a firm to engage in currency, interest rate, and other swap contracts?
a. The firm wants to raise its hedging costs by minimizing its exposure to currency exchange rate risk and interest rate risk.
b. The firm may use fixed-for-floating interest rate swap contract because it wants to align the returns from its assets with the payments on its liabilities.
c. An inefficiency in the global credit markets may provide a firm a comparative advantage to borrow money in a different currency and then engage in an interest rate swap to lower its borrowing costs and avoid currency exchange rate risk.
d. All of the above (a,b,c ) are valid reasons for firms to engage in swap contracts.
e. None of the above, except b and c, are valid reasons for firms to transact swap contracts.
Q 4. If the volatility of the underlying asset and option expiration time increases, then the:
a. Value of the put option will increase, but the value of the call option will decrease.
b. Value of the put option will decrease, but the value of the call option will increase.
c. Value of both the put and call options will increase.
d. Value of both the put and call options will decrease.
e. Value of both the put and call options will remain the same.
Q 5. Which statement is correct about the European option prices estimated from the binomial model and Black-Scholes-Merton (BSM) model (assume same exercise price, expiration time, and underlying stock)?
a. The option prices calculated from the binomial model can never be same as those calculated from the BSM model.
b. As the number of periods in a binomial model situation approaches infinity, the option prices estimated from the binomial model will approach (nearly equal to) those estimated from the BSM model.
c. As the number of periods in a binomial situation approaches infinity, the difference of the option prices estimated from the binomial model and BSM model will get larger.
d. Since binomial model assumes only two outcomes in each period, there should not be any relation between the option prices estimated from the binomial and BS models regardless of the number of periods in a given time to expiration.
Q 6. Company A can issue floating-rate debt at LIBOR + 1%, and it can issue fixed rate debt at 9%. Company B can issue floating-rate debt at LIBOR + 1.5%, and it can issue fixed-rate debt at 9.4%. Suppose A issues floating-rate debt and B issues fixed-rate debt, after which they engage in the following swap: A will make a fixed 7.95% payment to B, and B will make a floating-rate payment equal to LIBOR to A. What are the resulting net payments of A and B?
a. A pays a fixed rate of 9%, B pays LIBOR + 1.5%.
b. A pays a fixed rate of 8.95%, B pays LIBOR + 1.45%.
c. A pays LIBOR plus 1%, B pays a fixed rate of 9.4%.
d. A pays a fixed rate of 7.95%, B pays LIBOR.
e. None of the above answers is correct.
Q 7. If the volatility (σ) of a non-dividend paying stock is 25% per annum and a risk-free rate is 5% per annum, which of the following is closest to u (upward price change) for a binomial tree with a 6-month time step (at=0.5)?
A. 1.05
B. 1.07
C. 1.19
D. 1.11
Q 8. When dividends increase with all else remaining the same, which of the follow
D. Puts increase in value while calls decrease in value
C. Calls increase in value while puts decrease in value
B. Both calls and puts decrease in value
A. Both calls and puts increase in value ing is true?
Q 9. Which of the following is measured by the VIX index?
A. Implied volatilities for stock options trading on the CBOE
B. Historical volatilities for stock options trading on CBOE
C. Implied volatilities for options trading on the S&P 500 index
D. Historical volatilities for options trading on the S&P 500 index.
Q 10 Which of the following variables in the Black-Scholes-Merton option pricing model is the most difficult to obtain and thus is estimated?
a. the volatility
b. the risk-free rate
c. the stock price
d. the time to expiration
e. the exercise price
Q 11. Company X and Company Y have been offered the following rates
Fixed Rate Floating Rate
Company X 3.5% 3 month LIBOR plus 10bp
Company Y 4.5% 3 month LIBOR plus 30bp
Suppose that Company X borrows fixed and company Y borrows floating. If they enter into a swap with each other where the apparent benefits are shared equally, what is company X's effective borrowing rate?
A. 3-month LIBOR-30bp
B. 3.1%
C. 3-month LIBOR-10bp
D. 3.3%
Q 12. Ina binomial option pricing model, when moving from valuing an option on a non-dividend paying stock to an index option, which of the following is true for estimating uptick probability P?
A. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate in all calculations.
B. The formula for u changes.
C. The risk-free rate is replaced by the excess of the domestic risk-free rate over the dividend yield for discounting.
D. The risk-free rate be replaced by the excess of the foreign risk-free rate over the domestic risk-free rate when p is calculated.
Q 13. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. What is the downtick probability (1-P) that the stock price will be $26?
A. 0.6
B. 0.5
C. 0.4
D. 0.3
Q 14. In a floating oil price for fixed (guaranteed) oil price swap for an oil producing firm, the firm:
a. is worse off with the swap if oil price rises above the fixed price.
b. is able to remove the oil price risk which in similar to hedging risk.
c. is better off with the swap if oil price drops below the fixed price.
d. all of the above (a, b, and c).
Q 15. A company enters into an interrest rate swap where it is paying fixed and receiving LIBOR. When interest rates fall, which of the true?
A. The value of the swap to the company increase.
B. The value of the swap to the company decrease.
C. The value of the swap can either increase or decrease.
D. The value of the swap does not change providing the swap rate remains the same
Q16. Which of the following is a use of currency swap?
A. To exchange an investment in one currency for an investment in another currency.
B. T9o exchange borrowing in one currency for borrowings in another currency.
C. To take advantage situations where the tax rates in two countries are different.
D. All of the above.