May 22

Valuation of interest rate swap - 9 min screencast

by David Harper, CFA, FRM, CIPM

FRM |

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This screencast illustrates the valuation of an interest rates swap (following John Hull's procedure). Please note:

  • At inception, the value of the swap is zero or nearly zero
  • Under this approach, we simply treat the swap as two bonds: a fixed-coupon bond and a floating-coupon bond. The value of the swap is difference between the two.
  • A key idea relates to the value of the floating-coupon bond (segment): we don't need to value all of the cash flows, only the next cash flow. Why? At the next cash flow, the floating bond must be worth its par (or, in this case, the notional of $100 million). Since the coupons float with the same rate we use to discount the future cash flows, the present value of the floating series is the par.

Here is the screencast:

Comments

  1. klotfi 03 Jun 2008

    Thanks David for SC. One question. Shouldn’t we discount floating leg by three months LIBOR rather than six months LIBOR. If no, what is the logic of using six months when we are three months away from first cash settlement?

  2. David Harper, CFA, FRM, CIPM 03 Jun 2008

    klotfi - Yes, agreed, that single floating rate cash flow is three months out, so we PV at three months. Agreed on that. You will note I did discount 0.25 years at 5% (the three month rate).

    But the cash flow, in this case, is $2.75; half year based on 5.5% rate. So the “coupon” is based on six months rate because it pays in arrears. The SIZE of the cash flow look back six months, to a rate that prevailed six months ago (which here is 5.5% only b/c we assume the yield curve is static)

    David

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