Financial news

Pricing an interest rate swap means finding the fixed rate that equates the present value of the fixed payments to the present value of the floating payments, a process that sets the market value of the swap to zero at the start. Using the time line illustrated earlier, the swap cash flows will occur on days hl, h2,…,hn-l, and h,, so there are n cash flows in the swap. Day h, is the expiration date of the swap. The time interval between payments is m days. We can thus think of the swap as being on an m-day interest rate, which will be LIBOR in our examples.
As previously mentioned, the payments in an interest rate swap are a series of fixed and floating interest payments. They do not include an initial and final exchange of notional principals. As we already observed, such payments would be only an exchange of the same money. But if we introduce the notional principal payments as though they were actually made, we have not done any harm. The cash flows on the swap are still the same. The advantage of introducing the notional principal payments is that we can now treat the fixed and floating sides of the swap as though they were fixed- and floating-rate bonds.
So we introduce a hypothetical final notional principal payment of $1 on a swap starting at day 0 and ending on day h,, in which the underlying is an m-day rate. The fixed swap interest payment rate, FS(O,n,m), gives the fixed payment amount corresponding to the $1 notional principal.