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Q2. Mark Austin is a risk management consultant specializing in fixed income securities. He has been asked to evaluate the interest rate risk situation of an intermediate size bank. The bank has a large floating rate liability of $100,000,000 on which it pays the London Inter Bank Offered Rate (LIBOR) on a quarterly basis. Austin is concerned about the significant interest rate risk the bank incurs because of this liability. Since most of the bank's assets are invested in fixed rate instruments there is a considerable duration mismatch. Some of the bank's assets are floating rate notes tied to LIBOR. However, the total par value of these securities is significantly less than the liability position.
Austin considers both swaps and interest rate options. The interest rate options are 2-year caps and floors with quarterly exercise dates. He wishes to hedge the entire liability.
Austin has the technology to be able to generate an interest rate tree resulting in the quarterly incremented interest rate tree and the corresponding pricing tree for a two-year caplet shown in Table 1.
He has also obtained the prices for an at-the-money 6 month cap and floor with quarterly exercise. These are shown in Table 2.
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Table 1: Interest Rate Tree and Price Tree for Two-Year Caplet ($100M notional) |
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|
|
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12.23% |
|
|
|
|
|
|
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10.66% |
|
|
|
|
|
|
|
9.68% |
|
10.01% |
|
|
|
|
|
8.79% |
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8.72% |
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|
|
|
|
7.32% |
|
7.92% |
|
8.19% |
|
|
|
6.65% |
|
7.19% |
|
7.14% |
|
|
|
6.05% |
|
5.99% |
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6.48% |
|
6.70% |
|
5.00% |
|
5.45% |
|
5.89% |
|
5.84% |
|
|
|
4.95% |
|
4.91% |
|
5.31% |
|
5.48% |
|
|
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4.46% |
|
4.82% |
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4.78% |
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|
|
|
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4.02% |
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4.34% |
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4.48% |
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|
|
|
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3.95% |
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3.91% |
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|
|
|
|
|
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3.55% |
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3.67% |
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|
|
|
|
|
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3.20% |
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|
|
|
|
|
|
|
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3.00% |
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|
|
|
|
|
|
|
|
|
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|
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$1,557,206 |
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|
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$1,214,622 |
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|
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$933,050 |
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$1,001,459 |
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|
|
|
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$697,982 |
|
$741,758 |
|
|
|
|
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$507,549 |
|
$524,260 |
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$546,738 |
|
|
|
$357,476 |
|
$354,271 |
|
$348,281 |
|
|
|
$244,490 |
|
$231,189 |
|
$209,772 |
|
$174,677 |
|
$163,310 |
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$146,294 |
|
$121,961 |
|
$84,861 |
|
|
|
$90,294 |
|
$69,369 |
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$41,334 |
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$0 |
|
|
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$38,766 |
|
$20,180 |
|
$0 |
|
|
|
|
|
$9,892 |
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$0 |
|
$0 |
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|
|
|
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$0 |
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$0 |
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|
|
|
|
|
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$0 |
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$0 |
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$0 |
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$0 |
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Table 2:
At-the-Money 0.5 year Cap and Floor Values |
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Price of at-the-money Cap |
$133,377 |
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Price of at-the-money Floor |
$258,510 |
Austin analyzes alternative hedging strategies. Which of the following is the most appropriate transaction to most efficiently hedge the interest rate risk for a floating rate liability without sacrificing potential gains from interest rate decreases?
A) Buying a cap.
B) Selling a cap.
C) Buying a collar. | 
发表于 2009-4-2 10:18
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