Trader-Ready SOFR Swaption Pricing: Jamshidian Decomposition under the Hull–White Model

We propose a tractable SOFR-swaption pricing framework that integrates Jamshidian’s decomposition with the one-factor Hull–White model in the extended forward-measure/extended-bond setting, and derives closed-form formulae consistent with SOFR’s compounded-in-arrears convention. Model calibration generates a trader-ready σ-surface that supports interpolation across the expiry–tenor grid and facilitates pricing and mark-to-market valuation of less-liquid or bespoke contracts. Empirical results show good fit for short- and intermediate-maturity swaptions but significant errors for long-dated options, highlighting both the model’s practical value and its structural limitations.