Why SOFR Swaps Still Require Multiple Curves

Summary

The document asks why a multi-curve framework remains necessary after the transition from LIBOR to overnight risk-free rates. It outlines a common intuition: an OIS curve built from SOFR swaps can serve as the discount curve, and the quoted swap rates might appear sufficient to construct that single curve. The question contrasts this with the LIBOR framework, in which a separate forwarding curve and risk-free discount curve were used.

The text presents the questioner’s understanding rather than an answer or worked example. It therefore does not establish when a single curve is adequate or explain the market and instrument features that can require distinct discounting and projection curves. Its value is as a framing of curve construction and discounting assumptions for SOFR swaps; resolving the issue requires further explanation of collateral, floating-rate projection, and the instruments used to calibrate curves.

Key ideas

• The document distinguishes an OIS discount curve from the former LIBOR forwarding and discount curves.
• It asks whether SOFR swap rates alone can determine a single curve for discounting and projection.
• The discussion states a conceptual question but provides no answer or calibration example.
• Whether separate curves are needed depends on modeling and market conventions not examined here.

Tags

# OIS curve, why a multi-curve framework is needed


# OIS curve, why a multi-curve framework is needed












I don't understand why multi-curve framework is now needed.

Here is my understanding:

The OIS curve is now the curve considered risk-free, and it's used to discount the cashflows for example to value an IRS Swap that pays daily compounded SOFR.

This OIS curve is basically the SOFR curve. So the point at $t$-year is the compounded SOFR from now to $t$-years in the future.

These compounded SOFR term are estimated from Swaps that have annual paying frequency on the fixed leg, and annual paying frequency on the floating and pay daily compounded SOFR on the floating leg. So typically the $1$ Year swap rate will be the compounded SOFR for $1$ Year.

Now to find that curve we just need to solve an optimization problem where we observe the market price of these swaps and try to find the set of compounded SOFR such that our pricing model find the same market price using these compounded SOFR rates.

So why after Libor do we need dual curve building? Here for Swaps we just need one curve, the OIS curve (the SOFR curve).

Whereas during Libor we need two curves, the Libor curve and the discounting curve which is based on a RFR which I guess was EFFR at that time.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.