Caplets/Floorlets with Backward-Looking Risk-Free Rates under the One- and Two-Factor Hull-White Models

The transition from interbank offered rates (IBOR) to the new risk-free rates, and in particular the adoption of the backward-looking approach in place of the forward-looking one, affects the interest rate modeling and the pricing of interest rate derivatives. In this article, we introduce the pricing formula for caplets/floorlets with backward-looking risk-free rates under the one- and two-factor Hull-White model. In particular, we derive the appropriate volatility function for caplets/floorlets to be used in the pricing formula under the two-factor Hull-White model and, implicitly, under the one-factor Hull-White model. Our formulation allows us to obtain, as a particular case, the caplet/floorlet formula under the IBOR environment with a forward-looking rates approach. A numerical analysis is performed to illustrate the main feature of the proposed model and in order to provide a comparison in evaluating caplets/floorlets under both forward-looking and backward-looking approaches.