Post-LIBOR Swap Pricing: SOFR Projection and Discounting

# Market Convention to Price Interest Rate Swaps (post LIBOR transition)


# Market Convention to Price Interest Rate Swaps (post LIBOR transition)












Prior to the onset of the Global Financial Crisis in 2008, interest rate swaps were priced using a so-called "single curve framework". Under this framework, the LIBOR curve was used to estimate forward rates and to discount cash flows.

When the LIBOR / OIS spread blew out to ~365bp in Q4 2008, the market realized that LIBOR was a poor proxy for the risk-neutral discount rate. The market then transitioned to a dual-curve framework, with Fed Funds (in USD) used for cash flow discounting and the LIBOR curve used for forward curve estimation.

In the near future, LIBOR will be discontinued. In USD, the market is currently transitioning from LIBOR to SOFR underlyings.

How are interest rate swaps that reset against SOFR priced today? Are we once again back in the "single curve" framework, with the term SOFR curve used to estimate forward rates and to discount cash flows?

Thanks!

## Answer by KevinT (score 1, accepted)

https://quant.stackexchange.com/a/69419

It's an interesting question and I will try to answer from the European perspective, where (as of Jan 1 2022) we have moved away from CHF & GBP LIBORs. Basically, I would tackle this in two dimensions mainly (many other details I will leave out):

- New vs. old business (in projection dimension): new trades reference a compounded version of the SOFR index on the float leg, just like any other form of OIS does. Your existing LIBOR book can (a) either be "restructured" to reference compound SOFR + a spread (e.g. historical IBOR-SOFR basis) or (b) use the ISDA fallback clause for OTC derivatives (which is essentially the same as (a), it's just that ISDA gives you a heuristic on how to calculate the compound rate and also freezes the spread for you so that you can leave your legacy trade as is and still be able to let it expire by using this fallback reset).

- Secured vs. unsecured business (in discounting dimension): like you said, secured business would essentially move you back into some sort of single curve world, meaning SOFR (+ a spread, eventually) for projection, SOFR for discounting. In the uncollateralized world, it gets a bit more tricky, as there is no "risky" discount curve like the LIBOR IRS curve anymore once the index ceases. I've seen various approaches to this, e.g. discounting using the risk-free rate (SOFR), and add xVA charges based on the "true" cost of funding for your bank... or building a "legacy" LIBOR curve by simply shifting your OIS curve upwards by adding the (ISDA) spread... or - in case a derivatives market starts to pick up and is liquid enough for curve construction - use some other "credit-sensitive" rate index like Bloomberg BSBY, Ameribor Index, etc.

HTH