Interest Rate Swaps Explained From the Cash Flows Up

A swap's value comes from the present value of two separate cash flow legs, not from the fixed rate quoted on a screen.

An interest rate swap exchanges a stream of fixed payments for a stream of floating payments on the same notional amount, and its entire value comes down to the present value of those two cash flow streams. Understanding a swap starts with the cash flows themselves rather than with the swap rate quoted on a screen, since the quoted rate is simply the fixed rate that makes the two legs worth the same amount on the day the swap is agreed.

The fixed leg pays a set rate on a notional amount at agreed intervals, commonly quarterly or semiannually, for the life of the swap. The floating leg pays a rate that resets each period to a reference rate, historically LIBOR and now predominantly SOFR compounded over the period, plus or minus a small spread agreed at the outset. Neither leg exchanges the notional itself, since the notional exists only to size the coupon payments, which is why the instrument carries far less counterparty exposure than its size would suggest.

At the start of a plain vanilla swap, the fixed rate is set so the present value of the fixed leg exactly equals the present value of the floating leg, making the swap worth zero to either side at inception. That fixed rate is what gets quoted as the swap rate for that maturity, and a full set of swap rates across maturities is itself one of the primary inputs to the swap curve described in yield curve construction and bootstrapping.

Valuing the fixed leg is straightforward: discount every scheduled coupon back to today using the discounting curve, which since the shift away from LIBOR is generally an overnight indexed swap curve referencing SOFR. Valuing the floating leg requires projecting each future reset using forward rates read off a forecasting curve, then discounting those projected cash flows on the same discounting curve.

A useful shortcut for a freshly reset floating leg is that its value equals the notional itself, since the leg is economically equivalent to rolling a series of short-term deposits at the prevailing market rate each period. That shortcut breaks down between reset dates, which is exactly why desks maintain the dual curve framework, one curve to forecast the floating rate and a separate curve to discount every cash flow on both legs.