Chapter Thirteen
Swaps and Interest Rate Options
Answers to Problems and Questions
1. In an interest rate swap, the swap seller is the party paying the floating rate.
2. The swap tenor is the length (in time) of the swap arrangement. The swap
price is the fixed interest rate on the swap.
3. The only adjustments to the numbers in Figure 13-2 are that the big firm
would be paying 30 basis points more (LIBOR minus 20 bp instead of
LIBOR minus 50 bp) and the smaller firm would be paying 30 basis points
less. The net rates would be LIBOR – 20 for the big firm and 9.25% for the
smaller.
4. The larger firm often has the advantage in negotiating, either because of its
credit rating or its standing in the marketplace. The smaller firm, with less
bargaining power, may have to bear the cost of the fee in order to complete
the swap.
5. A swap is generally less risky than a loan because the principal amount
does not change hands. If one party defaults, the other party does not lose
any principal; they merely lose the advantage of the lower interest rate
payment.
6. The firm receiving the difference check would not logically default because
doing so would cause the other firm to cease sending them money. The
firm receiving the difference check pays no money out.
7. a)
duration gap = Dassets 
Total assets
x Dliabilities
Total liabilitie s
 300
  1200
  1400

x 0  
x 3.47   
x 8.43   5.51
 2900
  2900
  2900

Dassets = 
 900
  600
  400

x 1.0   
x 3.41  
x 10.00   3.11
 1900
  1900
  1900

Dliabilities = 
Duration gap = 5.51 
46
1900
x 3.66  3.11
2900
Chapter Thirteen. Swaps and Interest Rate Options
b) A positive duration gap means the bank is “asset sensitive.” If interest
rates rise, rate sensitive assets and liabilities will both fall in value, but
the asset side of the balance sheet will fall more. This means the bank’s
net worth will decline.
8. The bank can either reduce the duration of the asset side or increase the
duration of the liability side of the balance sheet. On approach would be to
swap the floating rate liability for a fixed rate liability of the appropriate
duration. First, find the duration of the liability side that would cause the
funds gap to be zero. Using the results from part a),
Dgap  5.51 
1900
Dliabilities  0
2900
Dliabilities = 8.41
We want to get the duration of the liabilities equal to 8.41 and we have
decided to do this by swapping the floating rate liability for a fixed rate
liability that has the duration we need. To find the duration, solve for Z in
the equation below.
 600
  400
  900

x 3.41   
x 10.00   
x Z   8.41

 1900
  1900
  1900

Z = 11.02
We would swap $900 floating rate for $900 fixed rate, where the fixed rate
instrument had a duration of 11.02. There are many combinations of
coupon and maturity that will produce this.
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Chapter Thirteen. Swaps and Interest Rate Options
9. Firm AAA pays 25 basis points less than BBB in the fixed rate market and
40 basis points less than BBB in the floating rate market. Therefore, AAA
has a comparative advantage in the floating rate market.
a) The diagram below shows one advantageous arrangement in which
AAA and BBB enter into a fixed for floating swap, but AAA enjoys all the
benefit.
5 YR + 80 bp
AAA
Libor + 40 bp
Libor
BBB
5 YR + 80 bp
Net: 5 YR + 40 bp
Net: Libor + 40 bp
In this scenario AAA winds up paying a fixed rate that is 40 basis points
lower than its market rate, while BBB pays a net rate equal to its market
rate. In order to motivate the deal, AAA would most likely receive less
than Libor + 40 bp from BBB, thereby splitting the benefits of the swap.
b) If AAA wants to borrow at a floating rate, there is no obvious advantage
to a swap with BBB. AAA’s rate is below BBB’s.
10. Because AAA pays less than BBB in both the floating and fixed rate
markets, AAA has an absolute advantage in both. AAA has a comparative
advantage in the floating rate market as the table below shows.
AAA
BBB
Difference
Fixed Rate
5 Yr + 60 bp
5 Yr + 80 bp
20 basis points
Floating Rate
Libor
Libor + 40 bp
40 basis points
11. There is some truth in this statement because of the possibility that one
currency may substantially depreciate relative to the other. While it is true
that if one party defaults on the return of the foreign currency principal the
other party will not return the principal on the other side, one currency may
be worth far less than the other at the end of the swap.
12. Individual response.
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Chapter Thirteen. Swaps and Interest Rate Options
13. a) A two-year 6% option would not provide protection for the entire tenor
of the swap. Because it is out-of-the-money and short-term, however, it
would be comparatively inexpensive.
b) A four-year 5.52% option would provide coverage for the duration of
the swap, but because it provides protection against any increase in rates
it would be expensive.
c) A four-year 6.25% cap would provide protection for the duration of the
swap, but it is substantially out-of-the-money and would provide little
protection. It would, however, be inexpensive.
d) A five-year 7% cap outlives the swap and involves more time value than
necessary. It is far out of the money, would be inexpensive, but would
provide little protection.
14. Writing a floor has the advantage of bringing in premium income and
reducing the effective borrowing rate by this amount. However, in the
event of falling interest rates the payments to the floor holder would
increase the effective borrowing rate to the floor writer.
15. Individual response.
16. You can use options to generate income in addition to using them to
manage risk. If a firm felt that the swaptions market was unusually rich in
premium it might consider writing such an option because of a belief that
the benefits of the premium income outweighed the risk of exercise.
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