Discounting Uncollateralized Swaps After LIBOR

# Uncollateralised trades in Libor transition


# Uncollateralised trades in Libor transition












Consider an OTC derivative traded with no CSA agreement, i.e. the trade is uncollateralised. My understanding is that a Libor swap curve is used in this case to discount the cashflows for this derivative as that reflects the funding, see Fuji et al 2010. This discount curve is constructed in the usual multicurve paradigm of inputs OIS and Libor xM curves, then using say 3M Libor curve to discount the cashflows. In a collateralised trade I would use the OIS to discount instead of Libor.

What happens after Libor cessation to the discount curve, what is the fair discounting curve? A naive approach would be to use the fallback curve bootstrapped from OIS swaps + ISDA fallback spread, but this doesn't seem natural to me.

## Answer by Ami44 (score 5, accepted)

https://quant.stackexchange.com/a/63029

Two replacements for the 3M Libor curve are possible:

- Construct a new 3M Swap discounting curve by adding spreads on top of the SOFR curve. These spreads can be calibrated on uncollateralized 3M SOFR swaps.

- Discount all derivatives, regardless if collateralized or not, with the SOFR curve, which is the true risk free curve. The credit risk arising from not being collateralized will then be accounted for by the CVA or maybe other xVAs.

It is yet unclear (to me) which alternative will be more popular. The second is liked more by academics while practitioners might like to see something like a 3M swap curve. Having a 3M Swap curve might also ease the transition and make it easier to deal with legacy contracts

## Answer by ir7 (score 4)

https://quant.stackexchange.com/a/63036

To add to above answer, this GARP article is summarizing recent work on new benchmark indices that attempt to address what Libor was meant to ('fairly') cover, but RFR’s don't, namely (term, unsecured) funding and some credit sensitivity: Ameribor, AXI, US Dollar ICE Bank Yield Index etc.. One banker points out there that an index like SOFR “would plummet when our costs of funds go up” (SOFR, as a secured rate derived from overnight repo transactions, may tighten in volatile times, when market participants look for safety).

One complementary aspect is that an institution has to add its own funding spread to the ('fair', market average) funding rate (whatever that is). So far an institution would add that spread to LIBOR rate, now the institution (corporate treasury) would need to make up new spreads and add them to the OIS/RFR rate.

Finally, this down-to-earth BIS article explains why seeking benchmarks for funding may still be quite relevant, using the historical ‘switch’ in the late 1980s as example, when market participants moved away from using benchmarks based on US Treasury bill rates (the prototypical 'risk-free rate') to those based on eurodollar rates. The primary driver of this "benchmark tipping" (as the authors call it, if I understood correctly) was that, in seeking to manage asset-liability mismatches, banks found eurodollar rates a much closer approximation to their actual borrowing costs and lending rates than US T-bill rates.

UPDATE: Bloomberg made its move too with BSBY.