Swap Question

CFA Level II Derivatives
#1

Hello,

I am still a bit confused on the logic behind fixed-for-floating. One of the question was as follows:

  • 180-Day LIBOR (5%)
  • 360-Day LIBOR (6%)
  • 540-Day LIBOR (6.5%)
  • 720-Day LIBOR (7%)

After 180 days, they drop to the following:

  • 180-Day LIBOR (4.5%)
  • 360-Day LIBOR (5%)
  • 540-Day LIBOR (6%)

When you calculate the value of the swap, we first add up the new discount factors after 180days (0.9780, 0.9524, and 0.9174) and multiply them by the fixed rate side of $0.0331 which is calculated using the old rates. This part I do not understand.

I also do not understand why this is added to the multiplication of $1 * 0.9174 which is the 540-day LIBOR rate. I’ve been solving previous sample questions and they made sense to me up until now. I have never seen this calculation before.

If you can please help me understand, that would be great.

Thank you!

#2

A plain vanilla interest rate swap is equivalent to two bonds; you’re long one bond and short one bond; one bond has a fixed rate and the other has a floating rate.

To price a swap, you equate the present value of the fixed-rate bond to the present value of the floating-rate bond and solve for the coupon rate.

To value a swap, you calculate the present value of the fixed-rate bond and the present value of the floating-rate bond. The present value of the fixed-rate bond will be each of the (known) coupon payments discounted back to today using the discount rates (that’s why you’re multiplying the fixed rate by the sum of the discount factors) plus the par value discounted back to today using the last discount factor (that’s the last bit: $1 is the assumed par value of bonds).