Options Futures and Other Derivatives 10th Edition By JohnC. – Test Bank
Hull: Options, Futures and Other Derivatives, Tenth Edition
Chapter 4: Interest Rates
Multiple Choice Test Bank: Questions with Answers
- The compounding frequency for an interest rate defines
- The frequency with which interest is paid
- A unit of measurement for the interest rate
- The relationship between the annual interest rate and the monthly interest rate
- None of the above
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.
- An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continuous compounding?
The equivalent rate with continuous compounding is ln(1.06) = 0.0583 or 5.83%.
- An interest rate is 5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding?
The equivalent rate with semiannual compounding is 2×(e0.05/2−1) = 0.0506 or 5.06%.
- An interest rate is 12% per annum with semiannual compounding. What is the equivalent rate with quarterly compounding?
The equivalent rate per quarter is. The annualized rate with quarterly compounding is four times this or 11.83%.
- 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.
The forward rate for the third year is (3×0.065−2×0.06)/(3−2) = 0.075 or 7.5%.
- 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?
If the rate is R we must have
so that R = ln(1/0.9137) = 0.0902 or 9.02%.