How to Price an Interest Rate Swap

An interest rate swap is an exchange between different cash flows. One cash flow stream is fixed and the other variable, but they both revolve around the current cost of money, or the interest rate. Market dynamics that affect the price of interest rate swaps are changes in interest rates over time, changes in interest rate swap spreads, FX rates, and the yield curve. Transaction specific variables which affect pricing are the notional amount of the swap, payment frequency, and time to maturity.

Things You'll Need

• Financial Calculator Spreadsheet Software

Instructions

1. Review the yield curve. Let's look at the yield curve for 10-year treasuries. The X axis of the yield curve is the time period. The Y axis is time to maturity. The alignment of the two variables is referred to as the yield curve. Each fixed income product has its own yield curve, however, U.S. treasuries are often cited as a benchmark. See Resources for current data points to the 10-year treasury yield curve.

2. Forecast future short-term rates. The uncertainty of forward rates makes the floating rate portion of the interest rate swap the more difficult side to value. A forward-looking yield curve with short-term interest rates is needed. This can be a continuation of Step 1.

3. Determine discount factors. Use the yield curve to find out the forward interest rates used to discount the future cash flows back to a present value.

4. Find the difference between the present value of fixed and floating cash flows. The formula is: PV = FV / (1+i)^n, where PV is the present value of cash flows, FV is the value of cash flows at time n, i is the discount rate, and n is the time period. This formula is programed into most financial calculators and spreadsheet software applications.

5. For example: The fixed leg of an interest rate swap consists of $1,000 payments at a rate of 5% over 2 years, and the variable rate swap consists of $1,500 payments at a rate of a 2-year treasury (from yield curve) plus 3% over a 2-year period. If the yield curve is showing treasuries at 3%, then inputting this information into the PV formula renders $1,859.41 for the fixed leg, and $2,750.09 for the variable rate PV. The difference provides the relative value or the price of the swap for the fixed leg portion. The variable leg usually pays more to compensate for the increased risk of variability.

References

• Undertanding the Time Value of Money

Resources

• Read this Article in Spanish
• US Treasury: Daily Rates