5.28.2005

Q&A: What's the swap value 90 days into its life...

...given the following 3-mon LIBOR term structure? The first floating payment was set at the 180-day rate of 9%.

Term (days) Rate
90 9.125%
270 10%
450 10.375%
630 10.625%

A

  • The new LIBOR terms to used are 6m-90=3m, 9m, 15m, and 21m.
Term (days) Spot LIBOR Rate Discount Factor
90 3m LIBOR = L(90, 90) = 9.125% B(90, 180) = 1 / (1+L(90, 90)*(90/360)) = 1 / (1+9.125%*(180/360)) = 0.9777
270 9m LIBOR = L(90, 270) = 10% B(90, 360) = 1 / (1+L(90, 270)*(270/360)) = 1 / (1+10%*(360/360)) = 0.9302
450 15m LIBOR = L(90, 450) = 10.375% B(90, 540) = 1 / (1+L(90, 450)*(450/360)) = 1 / (1+10.375%*(540/360)) = 0.8852
630 21m LIBOR = L(90, 630) = 10.625% B(90, 720) = 1 / (1+L(90, 630)*(630/360)) = 1 / (1+10.625%*(360/360)) = 0.8432
  • PV(fixed) = (180/360) x 0.0975 x (0.09777 + 0.09302 + 0.8852 + 0.8432) + 1 x 0.08432 = 1.02046963.
  • PV(floating) = (0.045 + 1) x (0.9777) = 1.0216965
    • the first floating payment was set at the 180-day rate of 9%. For a $1 notional principal, the payment would be 0.09 x (180/360) = 0.045
    • The value of the floating payments, is based on discounting the next floating payment of 0.045 and the market value of the floating-rate bond on the next payment date (which is $1)
  • PV(Swap) = (1.0216965 - 1.0204693) * $20 mil = $24,537.

Category: C++ Quant > Derivatives > Swaps

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