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

	2 months ago	1 month ago
3-month LIBOR	4.0% p.a.	4.2% p.a.
6-month LIBOR	4.6% p.a.	5.3% p.a.

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

	4 months from today	10 months from today
3-month LIBOR	6.0% p.a.	6.3% p.a.
6-month LIBOR	6.5% p.a.	7.0% p.a.

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

Maturity	LIBOR	Maturity	LIBOR
1	5.7% p.a.	6	6.2% p.a.
2	5.8% p.a.	7	6.3% p.a.
3	5.9% p.a.	8	6.4% p.a.
4	6.0% p.a.	9	6.5% p.a.
5	6.1% p.a.	10	6.6% p.a.

For example, the current 3-month LIBOR rate is 5.9% p.a. compounded continuously.

Required:

Calculate the current price of the security. Show all working.