Deck 21: Interest Rate Options

Question 1

In a floor with semiannual reset dates, the floor rate is 3.5% per annum and the notional principal is $1 million. Suppose that the LIBOR rate is 3% per annum for a particular 6-month period. What is the approximate payoff at the end of the 6 months?

A) $10,000
B) $5,000
C) $2,500
D) $1,250

Answer 1

C

Question 2

The price of a December put futures option is quoted as 5-52. Each Treasury bond futures contract is for delivery of $100,000 in Treasury bonds. What is the cost of one contract?

A) $5,520.00
B) $5,812.50
C) $6,625.00
D) $8,250.00

Answer 2

B

Question 3

A floating-rate borrower wants to use a collar as a hedge. Which of the following is appropriate?

A) Buy a cap and sell a floor
B) Buy a cap and buy a floor
C) Sell a cap and sell a floor
D) Sell a cap and buy a floor

Answer 3

A

Question 4

Which of the following is assumed to be lognormal when a swap option is valued?

A) A future bond price
B) A future swap rate
C) A future short-term rate
D) A future bond yield

Question 5

Which of the following is an implication of the mean reversion of interest rates?

A) Interest rates cannot become negative
B) When short-term interest rates are high they tend to move down
C) The term structure of interest rates tends to be upward sloping
D) When short-term interest rates are low they tend to stay low

Question 6

A ten year interest rate cap has quarterly resets. How many caplets does the cap consist of?

A) 38
B) 39
C) 40
D) 41

Question 7

A five-year cap is reset annually period. The cap rate is 3% and the notional principal is $100 million. The 12-month LIBOR interest rate for the third year proves to be 5%. Which of the following is approximately true?

A) The resulting payoff is $2 million at the beginning of the third year
B) The resulting payoff is $2 million at the end of the fifth year
C) The resulting payoff is $2 million at the end of the third year
D) The resulting payoff is $2 million half way through the third year

Question 8

Which of the following is true?

A) A callable bond allows the lender to ask for the principal to be repaid early
B) A callable bond allows the borrower to repay the principal early
C) A callable bond is a bond with an embedded stock option
D) None of the above

Question 9

In a cap with quarterly reset dates, the cap rate is 3.5% per annum and the notional principal is $1 million. Suppose that the LIBOR rate is 4.0% per annum for a particular 3-month period. What is the approximate payoff at the end of the 3 months?

A) $10,000
B) $5,000
C) $2,500
D) $1,250

Question 10

Which of the following is true?

A) A swaption that gives the holder the right to pay fixed is equivalent to a call option on a bond
B) A swaption that gives the holder the right to pay fixed is equivalent to a put option on a bond
C) A swaption that gives the holder the right to pay fixed is equivalent to a put option on one bond combined with a call option on another bond
D) None of the above

Question 11

A Eurodollar futures option contract has a strike price of 97 and the Eurodollar interest rate is 2.50%. What is the intrinsic value of the contract if the option is a put?

A) $0
B) $1,250
C) $1,750
D) $2,500

Question 12

In put-call parity for caps and floors, which of the following is true?

A) Long cap plus long floor equals swap
B) Long cap plus swap equals short floor
C) Long cap equals long floor plus swap
D) Long cap minus long floor equals swaption

Question 13

Which of the following is assumed to be lognormal when a bond option is valued?

A) A future bond price
B) A future swap rate
C) A future short-term rate
D) A future bond yield

Question 14

Which of the following is true?

A) A cap is a portfolio of put options on interest rates
B) A cap is a put option on a coupon-bearing bond
C) A cap is a call option on a coupon-bearing bond
D) None of the above

Question 15

A floating-rate lender wants to use a collar as a hedge. Which of the following is appropriate?

A) Buy a cap and sell a floor
B) Buy a cap and buy a floor
C) Sell a cap and sell a floor
D) Sell a cap and buy a floor

Question 16

Which of the following is true?

A) A puttable bond allows the lender to ask for the principal to be repaid early
B) A puttable bond allows the borrower to repay the principal early
C) A puttable bond is a bond with an embedded stock option
D) None of the above

Question 17

What is exchanged when a put option on an interest rate futures is exercised?

A) A long position in a futures contract for the holder of the option and a short position in a futures contract for the option writer
B) A short position in a futures contract for the holder of the option and a long position in a futures contract for the option writer
C) Cash payoff, a long position in a futures contract for the holder of the option, and a short position in a futures contract for the option writer
D) Cash payoff, a short position in a futures contract for the holder of the option, and a long position in a futures contract for the option writer

Question 18

A Eurodollar futures option contract has a strike price of 97 and the Eurodollar interest rate is 2.50%. What is the intrinsic value of the contract if the option is a call?

A) $0
B) $1,250
C) $1,750
D) $2,500

Question 19

Which of the following is assumed to be lognormal when a caplet is valued?

A) A future bond price
B) A future swap rate
C) A future short-term rate
D) A future long-term rate

Question 20

At the maturity of a bond option, it is estimated that the underlying bond will have a duration of 6 years and a yield of 5%. The forward yield volatility is quoted as 25%. What is the volatility of the forward bond price?

A) 3%
B) 30%
C) 20.8%
D) 7.5%