Short-rate models with stochastic discontinuities: A PDE approach

Alessandro Calvia, Marzia De Donno, Chiara Guardasoni and Simona Sanfelici

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 129-156

Abstract: With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (€STR) in Europe. These rates exhibit characteristics like jumps and spikes which correspond to specific market events, driven by regulatory and liquidity constraints. To capture these characteristics, this paper considers a general short-rate model that incorporates discontinuities at fixed times with random sizes. Within this framework, we introduce a PDE-based approach for pricing interest rate derivatives and establish, under suitable assumptions, a Feynman–Kač representation for the solution. For affine models, we derive (quasi) closed-form solutions, while for the general case, we develop numerical methods to solve the resulting PDEs.

Keywords: Overnight interest rate; Stochastic discontinuities; Interest rate derivatives; PDE approach; Affine models; Green’s function; Finite-difference method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:129-156

DOI: 10.1016/j.matcom.2026.04.034

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