Swap Valuation: Discounting Fixed and Floating Cash Flows

Key Takeaways

• Swap valuation equals PV(fixed leg) minus PV(floating leg); the fixed payer profits when market rates rise above the original swap rate, because the floating leg received is now worth more.
• The post-2008 multi-curve framework requires separate curves for forecasting SOFR floating payments and for discounting all cash flows at OIS rates, using a single curve is now a pricing error.
• Using the floating-leg shortcut (it prices near par at each reset) only works for uncollateralized swaps on a reset date; in any other case, full forward-rate pricing is required.
• Day-count mismatches between the fixed leg (typically 30/360) and the floating SOFR leg (ACT/360) produce real dollar differences on large notionals that single-convention models miss.

What It Is

A plain-vanilla interest rate swap has a fixed leg and a floating leg. Each leg is a schedule of future payments. Valuing the swap means discounting both schedules to today's present value and subtracting.

Swap value = PV(fixed leg) - PV(floating leg)

From the fixed-rate receiver's perspective, a positive number means the swap is an asset. From the fixed payer's perspective the sign flips. The market value of an existing swap is therefore a function of how current rates compare to the rate locked in at trade date.

The Intuition

At the moment a swap is struck, the fixed rate is set so that both legs are worth exactly the same. Neither party pays or receives anything to enter. That equilibrium rate is the swap rate, and it embeds current expectations of the floating benchmark over the swap's life.

Once a day passes, the yield curve has moved. The floating leg can still be thought of as a series of forward rates, but those forwards are now different. The fixed leg, on the other hand, is locked. The difference between the two streams is no longer zero, and the swap has real economic value.

How It Works

Discounting matters as much as forecasting. After the 2008 crisis, the market moved to a multi-curve framework. The floating leg's expected payments are estimated using a forward SOFR curve. Every cash flow on both legs is then discounted using the SOFR OIS curve rather than the same forecasting curve.

PV(fixed leg) = sum over i of ( K * tau_i * D_i )
PV(float leg) = sum over i of ( F_i * tau_i * D_i )

Where K is the fixed swap rate, F_i is the forward SOFR rate for period i, tau_i is the day-count fraction, and D_i is the OIS discount factor to the payment date.

OIS discounting is used because cleared and collateralized swaps earn interest on posted collateral at a rate tied to the overnight index. Discounting at anything else would misprice the collateral cash flows.

Worked Example

A $50 million 2-year pay-fixed swap was struck six months ago at a fixed rate of 3.80 percent. Today, 18 months remain. Assume the market now prices the remaining forward SOFR rates at 4.50, 4.40, 4.30 and 4.20 percent for each of the four remaining quarters, and OIS discount factors of 0.989, 0.978, 0.967 and 0.956.

Floating leg PV per quarter uses forward rate * 0.25 * $50M * discount factor. The four pieces sum to roughly $2.70 million.

Fixed leg PV per quarter uses 3.80% * 0.25 * $50M * discount factor. The four pieces sum to roughly $1.87 million.

From the fixed payer's viewpoint the swap value is PV(floating received) - PV(fixed paid) = $0.83 million. The payer is in the money because rates rose after trade date, so the floating leg they receive is now worth more than the fixed they owe.

Common Mistakes

1. Using one curve for both forecasting and discounting. This was the pre-crisis standard. It is now wrong. Forward rates come from the SOFR projection curve; discounting uses the SOFR OIS curve, and the two can diverge in stressed markets. A single-curve model will misprice collateralized swaps.

2. Valuing the floating leg as if it pays par at each reset. That shortcut works only for an uncollateralized swap on reset day, where the remaining floating leg value reduces to notional minus the PV of a zero-coupon bond. Outside that narrow case, full forward-rate pricing is needed.

3. Ignoring credit and funding adjustments. Uncleared bilateral swaps need CVA (credit valuation adjustment) and FVA (funding valuation adjustment) on top of the textbook value. These can be several basis points and matter for long-dated trades with thinly capitalized counterparties.

4. Mismatching day-count conventions between legs. USD fixed legs often use 30/360 while USD SOFR floating legs use ACT/360. Forcing both through the same convention produces small but real errors, especially on large notionals over many resets.

5. Forgetting that the swap rate and zero-coupon rate are different. A 5-year swap rate is a par rate on a stream of cash flows, not a single zero-rate. Bootstrapping a zero curve from par swap quotes is a required preprocessing step.

Frequently Asked Questions

Q: What is swap valuation in simple terms? Swap valuation is the process of calculating what an existing interest rate swap is worth right now. You discount each future fixed payment and each future floating payment to today's dollars, then take the difference. If current rates are above your locked-in fixed rate, the pay-fixed position is worth money to you.

Q: How does swap valuation affect investment decisions? A portfolio manager entering or exiting a swap mid-life needs an accurate mark-to-market value to know the true cost of unwinding. Mis-valuing a swap, especially by using pre-2008 single-curve methods, can leave a fund with a materially incorrect picture of its rate risk.

Q: What is a real-world example of swap valuation? A $50 million pay-fixed swap struck at 3.80% six months ago now has 18 months remaining. Today's forward SOFR rates have risen to 4.20 to 4.50%. The floating leg the payer receives is now worth more than the fixed payments owed, producing a mark-to-market gain of approximately $830,000.

Q: How can investors use swap valuation to manage interest-rate risk? By marking swap positions to market daily, a treasury team can see in real time whether its rate hedges are working. When the mark-to-market gain on a receive-fixed swap matches the mark-to-market loss on a fixed-rate bond portfolio, the hedge is functioning as intended.

Q: How is swap valuation different from bond pricing? A bond has one cash-flow stream (fixed coupons plus par). A swap has two streams with opposite signs and no principal exchange. Bond pricing uses a single yield to discount all flows. Swap valuation uses a multi-curve framework, one curve to forecast floating payments, another to discount them, making it more complex.

Sources

1. FactSet. "Interest Rate Swap Valuation White Paper." Tom P. Davis. https://insight.factset.com/hubfs/Resources/White%20Papers/Interest_Rate_Swap_Valuation_WP.pdf
2. CME Group. "Pricing and Hedging USD SOFR Interest Rate Swaps with SOFR Futures." https://www.cmegroup.com/articles/2025/price-and-hedging-usd-sofr-interest-swaps-with-sofr-futures.html
3. ICMA. "The Interaction Between Repo and Interest Rate Swaps." https://www.icmagroup.org/assets/documents/Events/ICMA-workshop-repo-and-swapsfinal.pdf

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.