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.

  • $\begingroup$ Out of curiosity - how do you get to do trades without posting collateral? Or is this in reference to legacy trades? $\endgroup$
    – user42108
    Commented Apr 22, 2021 at 21:34
  • $\begingroup$ I believe this is at counterparty level, the comment in the answer below sums it up well. $\endgroup$ Commented Apr 23, 2021 at 8:11
  • $\begingroup$ Thanks. I take it from Jan's comment that uncollateralized trades would be with NFCs. From experience, I think the extent to which counterparties will do uncollateralized trades depends on the NFC's credit (rating but also the bank's own analysis). $\endgroup$
    – user42108
    Commented Apr 23, 2021 at 15:14

2 Answers 2


Two replacements for the 3M Libor curve are possible:

  1. 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.

  2. 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

  • 2
    $\begingroup$ For case 2, the uncollateralized trade would attract FVA (Funding Valuation Adjustment): typically, uncollateralized trades would be against less sophisticated counterparties. Imagine such trade is hedged against "the street" (and therefore the hedge is collateralized). If the uncollateralized trade is "in the money", the hedge is out of the money and collateral needs to be posted: this collateral needs to be funded (at the FTP curve rate). On the other hand, a collateralized trade hedged with another collateralized trade would not attract such FVA (think collateral rehypothication). $\endgroup$ Commented Apr 22, 2021 at 14:56
  • $\begingroup$ You mentioned 3M SOFR swaps but the convention for SOFR swaps is annual >1Y, so if I take the ISDA/BBG fallback spreads then which spreads do I add to the equivalent OIS swaps? Do I add the 3M fallback spread to every SOFR OIS swap? ON/1W/2W/.../1Y/18M/2Y/... OIS swaps $\endgroup$ Commented May 14, 2021 at 8:40

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.

  • $\begingroup$ Nice addition; I was wondering if you (or someone else) happens to know, how these indices (like BSBY) can be used to actually value a transaction. I see their replacement for IBORs as a daily-fixing index... but as long as nobody starts quoting BSBY-linked IRS, how would one build a BSBY curve so to value derivatives linked to the fixing? $\endgroup$
    – KevinT
    Commented Aug 3, 2021 at 16:18
  • $\begingroup$ @KevinT You are right. BSBY-linked securities and derivatives are needed to get a curve. They did start engaging in BSBY-SOFR basis swaps. I think interest in BSBY is growing. $\endgroup$
    – ir7
    Commented Aug 3, 2021 at 21:39

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