Caplet Pricing for Discrete Backward-Looking RFR Term Rates under the Hull-White Model by Daria Iunevich, Diana Kalikaeva :: SSRN

This paper develops an analytical framework for pricing caplets on backward-looking term rates derived from Risk-Free Rates (RFRs) under the Hull-White model. Improving upon existing literature, we replace continuous approximations of daily-compounded RFRs, common in prior studies, with exact discrete formulations. Specifically, we derive closed-form solutions for caplets based on discretely compounded term rates and introduce semi-analytical solutions for discrete arithmetic averages. Numerical experiments demonstrate that our discrete approaches significantly reduce pricing errors compared to traditional continuous approximations, enhancing valuation accuracy for financial instruments linked to benchmarks like SOFR and SONIA. The work also demonstrates how to incorporate payment settlement lags and deterministic basis spreads into the analytical pricing framework. These contributions provide robust and implementable tools for derivatives valuation in post-LIBOR financial markets, ensuring closer alignment with actual market conventions.