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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?

  1. 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)?

  2. 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).

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  • $\begingroup$ Hi, I think you could find rates and discount factors for all relevant curves at CME, ftp.cmegroup.com/span/archive/cme/irs/2021 $\endgroup$ Sep 1 at 6:33
  • $\begingroup$ Before delving into an answer: Are you (roughly) familiar with collateralisation and CSA discounting? $\endgroup$ Sep 1 at 7:09
  • $\begingroup$ I am familiar with the use of discounting and the switch to using OIS for collateralized Swaps rather than LIBOR based discounting factors. @Kermittfrog. $\endgroup$
    – Student
    Sep 1 at 7:29
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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.

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. enter image description here

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.

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  1. Yes you add it to the forward rate in the payoff, you do not add it to the OIS curve.
  2. 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.
  3. 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
  4. 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.
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  • $\begingroup$ Will the OIS Discounting curve still however be based on a daily basis, meaning that if you have an ois discounting curve on 1/09/2021, then you will have a one day Discount Factor on 1/09/2021, and then the next day on the discount curve 02/9/2021 will then be the 2 day discount factor ext? (or is my understanding of the curve incorrect?, THEN w.r.t your number 4. Does this mean that the market will use (mostly OIS curves based on SOFR), and with that said the same OIS curve can be used to discount a Swap agreement under LIBOR or SOFR regardless of the floating leg? $\endgroup$
    – Student
    Sep 1 at 9:06
  • $\begingroup$ Perhaps there is some more understanding on the OIS curve construction needed. OIS swaps have a floating leg as p43 of quant.opengamma.io/…. These swaps have maturities {1W, 2W, 3W, 1M, 2M,..., 11M, 12M, 15M, 18M, 2Y, 3Y,..., 50Y}, due to low liquidity on the longer end some may use LIBOR-OIS basis swaps but I don't think this is the case any more. Given the shortest maturity is 1W, interpolation is required to obtain the daily rates, but this is typically not needed in bootstrapping due to the compounded rates being a ratio of DFs. $\endgroup$ Sep 1 at 10:29
  • $\begingroup$ You typically store your discount curve on the above market pillars, if you need at pricing step the interpolated daily rates then these can be calculated. The OIS discounting curve reflects the cost of collateralising a swap, it doesn't matter if it is LIBOR or OIS. In a LIBOR swap your discount curve is still the OIS but forwards from LIBOR - this is known as the dual curve approach or multicurve. $\endgroup$ Sep 1 at 10:32
  • $\begingroup$ Will the single curve methodology apply to SOFR Swaps valuations since SOFR is risk-free (which was not the case for LIBOR post-2008 hence the switch to the multi-curve methodology), or will it make more sense to use the same multi-curve methodology during the initial transition phase when switching a contract from LIBOR to SOFR fallback rates, for consistency. $\endgroup$
    – Student
    Sep 1 at 14:55
  • $\begingroup$ Specifically w.r.t Legacy contracts (rather than a new contract that will automatically be issued using SOFR) $\endgroup$
    – Student
    Sep 1 at 15:13

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