Question 1

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

Accepted Answer

B

Question 2

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

Accepted Answer

B

Question 3

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

Accepted Answer

A five-year cap means that the cap will be in place for five years regardless of when it is breached. The cap rate is 3%, meaning that if the LIBOR interest rate exceeds 3%, the cap will be triggered. The notional principal is $100 million, which is the hypothetical amount on which the interest rate is being calculated.

Since the cap is reset annually, the cap for the third year will be the same as the cap for the first two years. Therefore, the cap rate for the third year is 3%. Since the 12-month LIBOR interest rate for the third year is 5%, the cap will be triggered, and the resulting payoff will be $2 million at the end of the third year.

Therefore, the correct choice is C. The resulting payoff is $2 million at the end of the third year.

Question 4

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

Accepted Answer

The cost of one put futures contract is calculated as follows: 
Cost per point x contract size x multiplier 
In this case, the contract size is $100,000 in Treasury bonds and the multiplier is 32. 
The cost per point is calculated by subtracting the smaller price from the larger price in the quote: 
52 - 5 = 47 
So the cost per contract is: 
47 x $100,000 x 0.01 (multiplier) = $47,000 
However, the question is asking for the cost of ONE contract, not the cost per point. 
To get the cost of one contract, we need to divide the total cost by the number of points in a contract: 
$47,000 / 8 (number of points in a contract) = $5,875 
Therefore, the best choice is B, which is the closest to $5,875.

Question 5

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

Accepted Answer

The answer of Which of the following is true?
A)A cap...

Question 6

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%

Accepted Answer

The answer of At the maturity of a bond option,it...

Question 7

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

Accepted Answer

The formula for the payoff of a floor is:
Payoff = notional principal x [max((floor rate - LIBOR rate), 0) x (time period/365)]
Plugging in the numbers given:
Payoff = $1,000,000 x [max((0.035 - 0.03), 0) x (6/365)]
Payoff = $1,000,000 x [0.005 x 0.0164]
Payoff = $82
Rounding to the nearest hundred, the approximate payoff is $100. Therefore, the best choice is C) $2,500 as this is the closest to the calculated payoff.

Question 8

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

Accepted Answer

The cap rate is 3.5% per annum, which means for each quarter, the cap rate is 0.875% (= 3.5%/4). If the LIBOR rate is 4.0%, and the cap rate is 0.875%, then the net interest rate is 3.125% (= 4.0% - 0.875%).

The notional principal is $1 million, and the net interest rate for the quarter is 3.125%, so the interest payment for the quarter is $31,250 (= $1 million x 3.125%). However, the cap limits the payment to $1,250 (= $1 million x 0.875%). Therefore, the approximate payoff at the end of the 3 months is $1,250.

Therefore, the best choice is D.

Question 9

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

Accepted Answer

A future swap rate is assumed to be lognormal when a swap option is valued. This is because swap rates are typically modeled as the sum of lognormal spot rates, making the distribution of swap rates lognormal. Future bond prices, short-term rates, and bond yields are not necessarily lognormal.

Question 10

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

Accepted Answer

The answer of A Eurodollar futures option contract has a...

Question 11

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

Accepted Answer

The answer of A ten year interest rate cap has...

Question 12

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

Accepted Answer

A swaption that gives the holder the right to pay fixed is equivalent to a put option on a bond. This is because the holder has the option to enter into a swap where they pay fixed and receive floating. If interest rates rise, the value of the fixed payments will decrease, making the option to pay fixed more valuable, similar to a put option on a bond.

Question 13

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

Accepted Answer

When a put option on an interest rate futures is exercised, the holder of the option receives a cash payoff and holds a short position in a futures contract. The option writer receives the opposite: a long position in a futures contract and pays out the cash payoff. Therefore, the correct answer is D.

Question 14

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

Accepted Answer

According to put-call parity for caps and floors, a long cap is equal to a long floor plus a swap. This relationship is based on the fact that a cap is equivalent to a portfolio of a call option and a short position in a Treasury bond, while a floor is equivalent to a portfolio of a put option and a long position in a Treasury bond. By combining a long floor with a swap, an investor can create a synthetic long cap position. Therefore, option C is true.

Question 15

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

Accepted Answer

The interest rate used to determine the value of a caplet is typically assumed to follow a lognormal distribution. This is because short-term rates tend to have higher volatility compared to long-term rates, and the lognormal distribution is commonly used to model financial variables that exhibit this type of volatility behavior. Therefore, the correct choice is C (a future short-term rate). The other answer choices are not typically assumed to be lognormal when valuing a caplet.

Question 16

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

Accepted Answer

The answer of Which of the following is assumed to...

Question 17

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

Accepted Answer

A callable bond allows the lender (bondholder) to ask for the principal to be repaid before maturity. This feature gives issuers (borrowers) the option to redeem the bonds when interest rates fall, which reduces their debt-servicing costs.

Question 18

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

Accepted Answer

A collar involves buying a cap to limit the maximum interest rate payable and selling a floor to offset the cost of the cap. Therefore, the lender needs to sell a cap and buy a floor to set the minimum interest rate payable. This will provide a range within which the interest rate payable is fixed. Buying a cap and selling a floor would not provide an effective hedge as it would eliminate the benefits of the cap by selling the floor. Therefore, option D is the appropriate choice.

Question 19

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

Accepted Answer

The answer of A floating-rate borrower wants to use a...

Question 20

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

Accepted Answer

For a put option, the intrinsic value is calculated as the strike price minus the Eurodollar futures interest rate. In this case, the intrinsic value would be 97 - 2.50% = 97 - 0.025 = 96.975, which is below the strike price, so the intrinsic value is $0.

Quiz 21: Interest Rate Options

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

Which of the following is true?

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?

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?

Which of the following is true?

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?

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?

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?

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

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

Which of the following is true?

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

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

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

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

Which of the following is true?

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

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

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?