Question

Suppose that OIS rates of all maturities are 6% per annum, continuously compounded. The one-year LIBOR rate is 6.4%, annually compounded and the two-year swap rate for a swap where payments are exchanged annually is 6.8%, annually compounded.

a. What is the LIBOR forward rate for the second year when LIBOR discounting is used and the rate is expressed with annual compounding?

b. What is the LIBOR forward rate for the second year when OIS discounting is used and the rate is expressed with annual compounding?

Answer 1

a

Let the principal amount be $ 100, let the two year forward rate be R

6.40*e(-0.06) + 106.40e(-2R) = 100

6.0273 + 106.40e(-2R) = 100

106e(-2R) = 100 + 6.0273

106e(-2R) = 106.0273

R = 0.07223

Therefore, the LIBOR forward rate for the second year when LIBOR discounting is used is 7.223%

b

The one year year LIBOR rate is 6.4% annually compounded and the two year swap rate for a swap where payments are exchanged annually is 6.80%

Meaning when a fixed rate is paid the value of that exchange per $ 100 of principal would be

100*(0.064-0.068)e^(-0.06*1)

100*(-0.004)*e^(-0.06)

100*(-0.004)*(0.9418)

($0.3767)

F would be the forward rate for the second year than we would have

(F-0.068)e^(-0.06*2) = 0.003767

(F-0.068)*0.8869 = 0.003767

0.8869F - 0.0603 = 0.003767

0.8869F = 0.003767+0.0603

F = 0.07225

Therefore, the LIBOR forward rate for the second year when OIS discounting is used and the rate is expressed with annual compounding is 7.225%