Interest Rate Swap Curve

The interest rate swap curve is the set of fixed rates at which standard interest rate swaps trade, plotted against their maturities, typically from one year out to 30 years or more. Each point is the par swap rate: the fixed rate that makes a new swap against a floating benchmark, such as SOFR in US dollars, worth zero at inception. Dealers, banks, investors and corporate treasurers use the curve to price swaps, value fixed-income instruments and measure interest rate risk.

The swap curve is one form of yield curve. It differs from the government bond curve because it reflects interbank and derivatives market conditions rather than the yields on sovereign debt. Since the move away from LIBOR, the main swap curves in many currencies reference overnight risk-free rates, while some markets, including the euro area with EURIBOR, still maintain term-rate curves alongside them.

A price list at a garage might show what it costs to rent a car for a day, a week, a month or a year. Reading along the list tells you how the price changes with the length of the rental.

The swap curve is a price list for fixing interest rates. It shows the fixed rate you would have to pay, today, to swap a floating rate for a fixed one for two years, five years, ten years and so on. Lenders and borrowers use it to price fixed-rate loans and bonds, and to see what the market expects interest rates to do over time.

Short maturities are taken from overnight and money market rates, futures and forward rate agreements, and longer maturities from quoted par swap rates. A process called bootstrapping turns these quotes into discount factors and forward rates for every date. For a simple annual-pay swap valued on a single curve, the par swap rate for maturity $n$ is:

• $S_n$ is the par swap rate for a swap maturing in year $n$.
• $DF_i$ is the discount factor for payment date $i$, the present value of one unit paid on that date.
• $\alpha_i$ is the year fraction of each fixed-rate period.

For example, with discount factors of 0.96 at one year and 0.92 at two years and annual periods, the two-year par rate is (1 − 0.92) ÷ (0.96 + 0.92) = 0.08 ÷ 1.88 ≈ 4.26 per cent. Since the 2008 financial crisis, dealers have used a multi-curve approach, discounting collateralised swaps on an overnight index curve and projecting floating payments from the relevant benchmark curve.

The difference between a swap rate and the yield on a government bond of the same maturity is the swap spread. It reflects bank credit and funding conditions, the supply of government bonds, balance sheet costs for dealers and demand from hedgers. Swap spreads were long positive, but long-dated US dollar swap spreads turned negative after 2008 and have often stayed below zero, partly because regulation made it more expensive for banks to hold government bonds. Investors watch swap spreads as an indicator of funding stress and relative value, alongside the credit spread on corporate debt.

• Pricing derivatives. Swaps, caps, floors and swaptions are valued from the curve, and margin at a central counterparty depends on these valuations.
• Pricing loans and bonds. Banks price fixed-rate loans and corporate bonds as a spread over the swap rate of the same maturity, and issuers often swap fixed-rate debt back to floating.
• Risk measurement. Desks compute basis point value by shifting the curve and measure yield curve risk by moving individual points.
• Bank balance sheets. Banks often discount cash flows on the swap curve when estimating economic value of equity and setting internal funding prices.

Like a government curve, the swap curve can be upward sloping, flat or inverted. An inverted swap curve, with short rates above long ones, usually signals that the market expects policy rates to fall. Forward rates derived from the curve show the market-implied path of the floating benchmark, although they also include term premiums and should not be read as pure forecasts.

The curve has limits as a benchmark. Long maturities can be thinly traded, different currencies and benchmarks give different curves, and building it requires choices on interpolation and instrument selection that can produce slightly different values across firms.