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发表于 2011-3-25 15:05 | 只看该作者

Reading 64: Interest Rate Derivative Instruments-LOS a 习题精

2011, interest, center, style, label
Session 17: Derivative Investments: Options, Swaps, and Interest Rate and Credit Derivatives
Reading 64: Interest Rate Derivative Instruments

LOS a: Demonstrate how both a cap and a floor are packages of options on interest rates and options on fixed-income instruments.

 

 

A cap on a floating rate note, from the bondholder’s perspective, is equivalent to:

A)
 owning a series of calls on fixed income securities.
B)
 writing a series of interest rate puts.
C)
 writing a series of puts on fixed income securities.

 

For a bondholder, a cap, which puts a maximum on floating rate interest payments, is equivalent to writing a series of puts on fixed income securities. These would require the buyer to pay when rates rise and bond prices fall, negating interest rate increases above the cap rate. Writing a series of interest rate calls, not puts, would be an equivalent strategy. Calls on fixed income securities would pay when rates decrease, not when they increase.

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2#
发表于 2011-3-25 15:05 | 只看该作者

A floor on a floating rate note, from the bondholder’s perspective, is equivalent to:

A)
 owning a series of puts on fixed income securities.
B)
 writing a series of interest rate puts.
C)
 owning a series of calls on fixed income securities.

A floor, which puts a minimum on floating rate interest payments is equivalent to owning calls on fixed income securities which will pay when interest rates fall. Owning interest rate puts, rather than writing them, would be equivalent to the floor. Puts on fixed income securities pay when interest rates increase.

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3#
发表于 2011-3-25 15:05 | 只看该作者

An issuer who wishes to issue a floating rate note with a collar would be equivalently issuing the note and:

A)
 buying a cap and selling a floor.
B)
 selling a cap and buying a floor.
C)
 buying a cap and a floor.

Issuing a floating rate note with a collar (a cap and a floor) is equivalent to issuing the note, buying a cap to put an upper limit on the interest cost, and selling a floor which would put a minimum on interest expense and offset the cost of the cap to some extent.

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4#
发表于 2011-3-25 15:07 | 只看该作者

Which of the following best describes an interest rate cap? An interest rate cap is a package or portfolio of interest rate options that provide a positive payoff to the buyer if the:

A)
 T-Bond futures exceeds the strike price.
B)
 reference rate is below the strike rate.
C)
 reference rate exceeds the strike rate.

An interest rate cap is a package of European-type call option (called caplets) on a reference interest rate.

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5#
发表于 2011-3-25 15:10 | 只看该作者
Bower shorts the floating rate bond given in Table 2. Which of the following will best reduce Bower's interest rate risk?

A)
 Buying an interest rate floor.
B)
 Shorting Eurodollar futures.
C)
 Shorting an interest rate floor.

If he adds a short position in Eurodollar futures to the existing liability in the correct amount, he is able to lock in a specific interest rate. A short Eurodollar position will increase in value if interest rates rise because the contract is quoted as a discount instrument so increases in rates reduce the futures price. (Study Session 17, LOS 62.a)

Bower has studied swaps extensively. However, he is not sure which of the following is the swap fixed rate for a one-year interest rate swap based on 90-day LIBOR with quarterly payments. Using the information in Table 1 and the formula below, what is the most appropriate swap fixed rate for this swap?

A)
 5.65%.
B)
 5.75%.
C)
 6.01%.

The swap fixed rate is computed as follows:

Z90-day =

1

1 + (0.055 × 90 / 360)

=

0.98644

Z180-day =

1

1 + (0.05625 × 180 / 360)

=

0.97264

Z270-day =

1

1 + (0.057499 × 270 / 360)

=

0.95866

Z360-day =

1

1 + (0.058749 × 360 / 360)

=

0.94451

The quarterly fixed rate on the swap =

1 ? 0.94451

0.98644 + 0.97264 + 0.95866 + 0.94451

= 0.05549 / 3.86225 = 0.01437 = 1.437%

The fixed rate on the swap in annual terms is:

1.437% × 360 / 90 = 5.75%

(Study Session 17, LOS 61.c)

Bower would like to perform some sensitivity analysis on a one year collar to changes in LIBOR. Specifically, he wonders how the price of a collar (buying a cap and selling a floor) is affected by an increase in the LIBOR forward rate volatility. Using the information in Tables 1 and 2 which of the following is most accurate? The price of the collar will:

A)
 increase.
B)
 decrease.
C)
 stay the same.

The price of the floor will increase more than the price of the cap since the floor is closer to being at the money than the cap. Therefore, the floor price is more sensitive to volatility changes in the LIBOR forward rate. Since the price of the collar is equal to the price of the cap minus the price of the floor, the net effect is a price decrease for the collar. (Study Session 17, LOS 62.a)

Bower computes the implied volatility of a one year caplet on the 90-day LIBOR forward rates to be 18.5%. Using the given information what does this mean for the caplet's market price relative to its theoretical price? The caplet's market price is:

A)
 undervalued or overvalued.
B)
 overvalued.
C)
 undervalued.

Volatility and option prices are always positively related. Therefore, since the option implied volatility is lower than the estimated volatility, this implies that the caplet is undervalued relative to its theoretical value. (Study Session 17, LOS 62.a)

For this question only, assume Bower expects the currently positively sloped LIBOR curve to shift upward in a parallel manner. Using a plain vanilla interest rate swap, which of the following will allow Bower to best take advantage of his expectations? Purchase a:

A)
 receive fixed interest rate swap.
B)
 floating rate bond and enter into a receive fixed swap.
C)
 pay fixed interest rate swap.

Since the interest rates are expected to rise for all maturities, one can benefit from this rise by receiving a floating rate (LIBOR) and borrowing at a fixed rate (i.e. a pay fixed swap). (Study Session 17, LOS 61.c)

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6#
发表于 2011-3-25 15:10 | 只看该作者

To the issuer of a floating rate note, a cap is equivalent to:

A)
 writing a series of interest rate calls.
B)
 owning a series of interest rate calls.
C)
 owning a series of calls on a fixed income security.

The issuer of the note is borrowing at a floating rate, and will have higher interest expenses if rates increase. A cap is equivalent to owning a series of interest rate calls at the cap rate that will pay the difference between the market rate and the cap rate. If interest rates increase, the payoff from the calls will compensate the borrower for the higher interest expenses.

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