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From books it looks like market standards to price IR options, like swaptions, are SABR, LMM or mix of the two (SABR-LMM). But LMM models the forward LIBOR rate. What will happen to it once LIBOR ceases to exists and only SOFR is traded in the market? Will this model still be valid somehow? Since SOFR is already here, is a new trend emerging when it comes to option pricing that might already suggest what will become the new market standard to price IR options?

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The industry will continue to use SABR and LMM, although in slightly modified versions. You may want to check the following papers to see how the extended model dynamics look like: SABR smiles for RFR caplets, Looking Forward to Backward-Looking Rates: A Modeling Framework for Term Rates Replacing LIBOR and Looking Forward to Backward-Looking Rates: Completing the Generalized Forward Market Model. The later is sometimes referred to as FMM (Forward Market Model) and led to its inventors being awarded the Quant of the Year in 2020, so it definitely worth reading.

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  • $\begingroup$ Thank you @Hasek, are you aware of any implementations of these new versions that is free to look at (Python or other languages)? $\endgroup$
    – Goo Gle
    Jul 18 at 14:47
  • $\begingroup$ @GooGle, the formulas from SABR smiles for RFR caplets are quite straightforward and you should have no problems coding them up in addition to vanilla SABR. Since you're referring to Python you may take a look at pysabr package. You may also modify an already existing LMM imlementation to incorporate RFRs, this is essentially what I'm doing right now as a sell-side desk quant, however I didn't come across any sufficiently good LMM implementation in open source projects. $\endgroup$
    – Hasek
    Jul 19 at 10:31

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