Reference no: EM133059681
Several months ago, Buddy Inc. issued a unique fixed income security. As of today, the security is maturing in 10 months.
The security pays semi-annual interest, which is equal to X% minus 3% p.a., where X is equal to the sum of the 6-month and 3-month LIBOR rates. That is, in every six months, the interest is defined as:
where L6 (quoted on an annual basis, in %) is the 6-month LIBOR and L3 (also quoted on an annual basis, in %) is the 3-month LIBOR. Assume that the 6-month LIBOR is always greater than the 3-month LIBOR and the 3-month LIBOR is always greater than 3% p.a. At maturity, the company will pay $100 as the face value of the security. Also, assume all other bonds and floating rate notes have a face value of $100, respectively.
Table 1 shows the 3-month and 6-month LIBOR rates observed several months ago:
Table 1
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2 months ago
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1 month ago
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3-month LIBOR
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4.0% p.a.
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4.2% p.a.
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6-month LIBOR
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4.6% p.a.
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5.3% p.a.
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For example, two months ago, the 3-month LIBOR rate was observed at 4.0% p.a.
Table 2 shows the predicted 3-month and 6-month LIBOR rates over the next few months:
Table 2
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4 months from today
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10 months from today
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3-month LIBOR
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6.0% p.a.
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6.3% p.a.
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6-month LIBOR
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6.5% p.a.
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7.0% p.a.
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For example, four months from today, the 3-month LIBOR rate is predicted equal to 6.0% p.a.
Table 3 shows the current LIBOR rates (assume continuous compounding) with different maturities over the next 10 months:
Table 3
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Maturity
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LIBOR
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Maturity
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LIBOR
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1
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5.7% p.a.
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6
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6.2% p.a.
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2
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5.8% p.a.
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7
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6.3% p.a.
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3
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5.9% p.a.
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8
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6.4% p.a.
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4
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6.0% p.a.
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9
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6.5% p.a.
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5
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6.1% p.a.
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10
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6.6% p.a.
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For example, the current 3-month LIBOR rate is 5.9% p.a. compounded continuously.
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