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Given that LIBOR is being decommissioned and we must start building liquidity in swaptions on the OIS swaps, how do we price them? i.e. If I have a swaption on SONIA/SOFR/ESTR etc how does the pricing formula change from the classical single-curve formula? Let us assume we are in a backwards compounded in-arrears forward for the curve.

$$F_j (t)=\frac{1}{τ_j (t)} \left(\prod_{i=1}^n\left(1+τ_i I^{ON} (s_{i-1})\right) -1\right)$$

https://www.risk.net/derivatives/6914531/dealers-dip-toe-into-sonia-swaptions-market

I would also be interested in cap/floors too.

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    $\begingroup$ A lot of this involve quite tedious calculations. I recommend you take a look at Marc Henrard's paper "A quant perspective on IBOR fallback approaches" (2018). Check out pages 26 through 28 for inspiration. $\endgroup$
    – Daneel Olivaw
    Oct 24 '19 at 10:29

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