Options Futures and Other Derivatives 10th Edition By JohnC. – Test Bank

Options Futures and Other Derivatives 10th Edition By JohnC. – Test Bank

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Hull: Options, Futures and Other Derivatives, Tenth Edition

Chapter 4: Interest Rates

Multiple Choice Test Bank: Questions with Answers

1. The compounding frequency for an interest rate defines
   1. The frequency with which interest is paid
   2. A unit of measurement for the interest rate
   3. The relationship between the annual interest rate and the monthly interest rate
   4. None of the above

Answer: B

The compounding frequency is a unit of measurement. The frequency with which interest is paid may be different from the compounding frequency used for quoting the rate.

1. An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continuous compounding?
   1. 5.79%
   2. 6.21%
   3. 5.83%
   4. 6.18%

Answer: C

The equivalent rate with continuous compounding is ln(1.06) = 0.0583 or 5.83%.

1. An interest rate is 5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding?
   1. 5.06%
   2. 5.03%
   3. 4.97%
   4. 4.94%

Answer: A

The equivalent rate with semiannual compounding is 2×(e^0.05/2−1) = 0.0506 or 5.06%.

1. An interest rate is 12% per annum with semiannual compounding. What is the equivalent rate with quarterly compounding?
   1. 11.83%
   2. 11.66%
   3. 11.77%
   4. 11.92%

Answer: A

The equivalent rate per quarter is. The annualized rate with quarterly compounding is four times this or 11.83%.

1. The two-year zero rate is 6% and the three-year zero rate is 6.5%. What is the forward rate for the third year? All rates are continuously compounded.
   1. 6.75%
   2. 7.0%
   3. 7.25%
   4. 7.5%

Answer: D

The forward rate for the third year is (3×0.065−2×0.06)/(3−2) = 0.075 or 7.5%.

1. The six-month zero rate is 8% per annum with semiannual compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate?
   1. 8.02%
   2. 8.52%
   3. 9.02%
   4. 9.52%

Answer: C

If the rate is R we must have

or

so that R = ln(1/0.9137) = 0.0902 or 9.02%.