Inferring the Implied Volatility of SOFR-Based Swaptions

The adoption of SOFR introduces valuation and hedging challenges for derivatives due to its backward-looking settlement style. Despite the availability of analytical pricing formulae for vanilla SOFR derivatives, the early-stage SOFR swaptions market impedes model implementation and empirical validation due to insufficient liquidity and lack of historical data. This article develops a mechanism to convert volatility quotes from actively traded LIBOR swaptions to emerging SOFR swaptions. The proposed mechanism facilitates the transfer of price information embedded in LIBOR-based swaptions to SOFR-based swaptions, contributing to the establishment of a crucial SOFR swaption market for trading volatilities associated with the new benchmark.