Is there a research showing a way to use SABR LMM with new RFRs such as SOFR, i.e. pricing exotic path-dependent RFR derivatives with volatility smile and skew?
I'm aware that
- 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 explains that classic LMM can be extended to handle RFR and IBOR-like rates simultaneously in a so called FMM (Forward Market Model)
- SABR Smiles for RFR Caplets presents an extension of the SABR model to price both backward and forward-looking vanilla RFR caplets
However I haven't seen anything regarding FMM with stochastic volatility. Does it mean we don't know yet how to price exotic RFR options or how to price vanilla RFR options simultaneously with exotic LIBOR options in one model?