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.