Arithmetic Average RFR Cap and Floor Valuation With the SABR Model

A model independent formula is derived for the valuation of a discrete arithmetic average RFR cap and floor in terms of an asymmetric quadratic option on the canonical daily compounded RFR index. The authors show how model independently our valuation formula can be expressed in terms of vanilla options and symmetric quadratic derivatives on the daily compounded RFR index to capture the necessary convexity adjustment.The results are then specialized to the case of the SABR model for an RFR index, where the authors provide a closed-form valuation formula in terms of market traded vanilla RFR caps and floors. Call-put parity is shown to be satisfied for the valuation formula.