Question

Cement Al-Yamamah has just entered into a two-year floating-for-fixed swap contract, where payments are made every six months. The 6-month LIBOR is 4.11%. The 6 to 12 months forward LIBOR rate is 5.92% and the 12 to 18 month forward LIBOR rate is 8.19. The two-year swap rate is 5.1%. If the OIS rate is 3.5% and the term structure of the OIS rate is flat, what is the 18 to 24 month Forward LIBOR rate? All rates are semi-annually compounded, except for the OIS, which is continuously compounded.

(Round to the closest hundredths. Rates should be in percentage form. E.g. 9.99%)

Cement Al-Yamamah has just entered into a two-year floating-for-fixed swap contract, where payments are made every six months. The 6-month LIBOR is 4.31%. The 6 to 12 months forward LIBOR rate is 5.59% and the 12 to 18 month forward LIBOR rate is 8.27. The two-year swap rate is 6.6%. If the OIS rate is 3.5% and the term structure of the OIS rate is flat, what is the 18 to 24 month Forward LIBOR rate? All rates are semi- annually compounded, except for the OIS, which is continuously compounded. (Round to the closest hundredths. Rates should be in percentage form. E.g. 9.99) Selected Answer: X 8.26% Correct Answer: 8.36 + 0.01 Response You need to find the present value of the first three payments in the Feedback: swap as if the floating rates are the LIBOR forward rates. Add the PV together. From-SUM(PV1, PV2, PV3) get what should be the 18- 24 forward LIBOR rate. Since the swap has just been signed, the sum of the present value of all four payments must be 0.

Answer 1

Suppose the two year swap rate is 5.1%.Swap can be valued by assuming that forward rates are realized..The value of first payment in the swap assuming principle of 100 is

0.5(0.0411-0.051)x100 x e-^0.035x0.5 = -0.4864

0.5(0.0592-0.051)x100x e^-0.035x1.0 = 0.3959

0.5(0.0891-0.051)x100x e^-0.035x1.5 =1.4659

Total value of first three payments = 1.3754

forward rate for final payment F is

0.5(F-0.051)x100xe^-0.035x2.0 =1.3754

F=0.07665

F=7.665%