Applying Credit Spreads and OIS Discounting in Multicurve Swap Valuation

# How to account for the credit spread ( e.g. LIBOR + 2%) when using the Multicurve Methodology in valuing a Swap


# How to account for the credit spread ( e.g. LIBOR + 2%) when using the Multicurve Methodology in valuing a Swap












When valuing an Interest rate swap, counterparties will typically issue the contract at a Libor + credit premium, e.g. Libor +2%. When valuing a swap, we require a LIBOR forward curve and Discounting curve. Under the multi-curve methodology, we have an OIS discounting curve and the forward curve based on LIBOR rates.

Question:

1. how do you account for the credit spread e.g. 2% in the LIBOR +2%? Do you simply add it to the forward curve rates (which is based on libor flat), and also to the OIS discounting curve, or only add it to the forward curve and not the discounting curve?

- Is the OIS discounting curve a daily compounded curve, i.e. there is a discounting factor for every day of the month in the curve (or are there different ways in which this curve can be represented in)?

- Are there any market/publically available OIS discounting curves published somewhere (free)?

4. With regards to the Transition to SOFR, will the same OIS discounting curve that was used to value swaps under a LIBOR agreement be used to value a swap that is transitioning to SOFR, (since the curve is not directly determined from the floating leg (libor)), Or will a different OIS discounting curve be constructed for valuing SOFR swaps in the transition, where the OIS discounting curve will be constructed out of OIS SOFR swaps?

(I saw that an OIS curve can be constructed using LIBOR swaps or SOFR swaps for the long end of the OIS discounting curve).

## Answer by AKdemy (score 4)

https://quant.stackexchange.com/a/66729

1 ) Spread is for fwd only

4 ) Discounting is SOFR in any case (if using dual curve). See here for some details. That said, FF OIS still exists, but even this curve is discounted by SOFR and applies "vanilla" dual curve stripping (in terms of Bloomberg jargon, S42 is discounted by SOFR S490). However, if you roll back the valuation date pre 2020-10-17 then it should automatically cut back to S42.

If you have purely SOFR, you do not have the classic dual curve anymore.

In May 2020, the ARRC published best-practice recommendations for completing the transition from LIBOR to SOFR for various classes of financial products, which you may find useful.

For swaps, it is important to study the contract’s details. Some are easier to change than others. For example, if you have a centrally cleared IRS, the clearinghouse can unilaterally change the baseline rate from LIBOR to SOFR. However, changing an over-the-counter derivative will likely require the approval of the counterparty. Especially important is the “fallback language” – the clause in the contract that specifies how rates and payments will be calculated should LIBOR cease publication. Particularly those contracts not drafted around guidelines set by associations like ISDA or the LSTA, are vague about how this works or may not have any provisions at all.

For new swaps, it seems many people think that there is no alternative to SOFR. Regulators recommend SOFR as the replacement for LIBOR, but also indicated that market participants are free to choose alternatives. In terms of credit risk post Libor, there exist credit sensitive benchmarks.

- ICE's Bank Yield Index

- Bloomberg's BSBY Index

For example, BSBY-SOFR basis swaps already trade for a while now. The BSBY index is dynamic, it incorporates a credit-sensitive element, and it reflects the marginal funding cost for banks across five different tenors (overnight, one month, three months, six months, and 12 months).

CME also trades BSBY futures now.

Bottom line is that I reiterate the comment I made here. I think the real question (for you) will be what you really need? It is not trivial to build a reliable curve infrastructure, even if you know all the details about the product. What data and tools do you have access to. If none, it may be worth to start asking (yourself) what the best available solutions are (in terms of your budget, usability, reliability).

For 2 ) and 3 ), see the answer of @BrownianBread.

Risk.net has a series (of Bloomberg sponsored) Libor transition videos.

Edit BSBY will be discontinued on November 15,2024 after a damning Iosco verdict, see Risk.net.

## Answer by BrownianBread (score 3)

https://quant.stackexchange.com/a/66717

- Yes you add it to the forward rate in the payoff, you do not add it to the OIS curve.

- The OIS curve is typically an ON rate compounded daily, the instruments you use to bootstrap this curve do not have daily maturities so interpolation is required when calculating the discount factor at non-market-pillar dates.

- I don't think there are free public OIS swaps available. There are some futures listed by CME here https://www.cmegroup.com/markets/interest-rates/stirs/three-month-sofr.quotes.html

- The interdealer market switched from using Fed Funds to SOFR as the default discount curve already, with more recent SOFR-first initiatives from the central banks/regulators, it has increased liquidity further down the curve meaning that using OIS-LIBOR basis swaps may no longer be necessary. Either way, due to the cessation of Libor, the reliance of the OIS-LIBOR swaps which entangles the two curves will become irrelevant soon.