Q1

Several months ago, Buddy Inc. issued a unique fixed income security. As of today, the security is maturing in 11 months. The security pays semi-annual interest, which is equal to X% p.a minus the 6 month LIBOR, where X% is equal to the sum of 6% p.a. and the 3-month LIBOR rate. That is, in every six months, the interest is defined as: 6% L3% L6% + 2 4 2 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 will never exceed 6% 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 in the previous months as follows: Table 1 2 months ago 1 month ago 3-month LIBOR 3.4% p.a. 3.1% p.a. 6-month LIBOR 3.7% p.a. 3.4% p.a. For example, two months ago, the 3-month LIBOR rate was observed at 3.4% p.a. Table 2 shows the predicted 3-month and 6-month LIBOR rates over the next few months: Table 2 5 months from today 11 months from today 3-month LIBOR 2.4% p.a. 2.6% p.a. 6-month LIBOR 2.5% p.a. 2.9% p.a. For example, five months from today, the 3-month LIBOR rate is predicted equal to 2.4% p.a. Table 3 shows the current LIBOR rates (assume continuous compounding) with different maturities over the next 12 months: Table 3 Maturity LIBOR Maturity LIBOR 1 2.7% p.a. 7 3.25% p.a. 2 2.8% p.a. 8 3.3% p.a. 3 2.9% p.a. 9 3.35% p.a. 4 3.0% p.a. 10 3.4% p.a. 5 3.1% p.a. 11 3.45% p.a. 6 3.2% p.a. 12 3.5% p.a. For example, the current 3-month LIBOR rate is 2.9% p.a. compounded continuously. Required: Calculate the current price of the security. Show all working