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We extend the short rate model of Turfus and Romero-Berm\'udez [2021] tofacilitate accurate arbitrage-free analytic pricing of SOFR, SONIA or ESTRcaplets, i.e. options on backward-looking compounded rates payments, in amanner consistent with the smile and skew levels observed in the market. Thesecaplet pricing formulae and corresponding LIBOR or term-rate caplet results aretranslated into effective variance (implied volatility) formulae, which areseen to be of a particularly simple form. They show that the model isessentially equivalent to imposing on a Hull-White model an effective variancewhich is a quadratic function of the moneyness parameter (rather than aconstant) for any given maturity. Results are also illustrated graphically.

Analytic RFR Option Pricing with Smile and Skew