Let us assume that LIBOR rates for 6 and 12 months are 3\% and \(3.3 \%\), respectively, with continuous compounding. We would like to find the LIBOR rate for 18 months, and we consider the quoted swap rate for a contract maturing in 18 months with semiannual payments. The quoted rates are

                        bid \(3.5 \% \quad\) ask \(3.7 \%\)

which reflect the bid-ask spreads observed in real-life markets (see Section 5.3.1). Let us take the average, \(3.6 \%\), as the swap rate. Note that these rates are to be considered as semiannually compounded and define cash flows, rather than discount factors. The swap rate is such that a fixed-coupon bond with coupon rate \(3.6 \%\), maturing in 18 months, trades at par. Assuming an arbitrary face value of \(\$ 1\), we have to solve the following equation:

which yields  with continuous compounding.

Transcribed Image Text:

0.036 0.036 1 -0.03x0.5 -0.033x1 + 2 2 + +(1+5 0.036 xe-L(0,1.5)1.5 2