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SABR LMM and Stochastic Volatility for RFR Derivatives

Article Quant Q&A · Author: Hasek
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Summary

The document asks whether a forward market model (FMM), extending the classic LIBOR market model to handle backward-looking risk-free rates (RFRs) and term rates together, has been combined with stochastic volatility such as SABR. The motivation is pricing exotic, path-dependent RFR derivatives while capturing volatility smiles and skew, and potentially pricing RFR and LIBOR options within one framework.

It points to prior work on FMM extensions and on SABR pricing for vanilla RFR caplets, but does not provide a proposed model, derivation, pricing results, or a definitive answer. Its evidence is therefore a description of related research rather than a demonstration that a combined SABR FMM is available or that exotic RFR options cannot be priced. The question highlights an open modeling and literature-search issue; conclusions about the state of the field would require consulting the referenced papers and subsequent research.

Key ideas

  • A forward market model can represent backward-looking RFRs alongside IBOR-like term rates.
  • The document identifies separate research on FMM extensions and SABR pricing for vanilla RFR caplets.
  • It asks whether stochastic volatility can be incorporated into an FMM for RFR derivatives.
  • The document does not establish whether exotic RFR options can be priced in such a model.

Tags

Fixed incomeOptionsVolatilityDerivatives pricing
Full text
# SABR LMM for RFR


# SABR LMM for RFR












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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.