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Short-rate models with stochastic discontinuities: A PDE approach

Author

Listed:
  • Calvia, Alessandro
  • De Donno, Marzia
  • Guardasoni, Chiara
  • Sanfelici, Simona

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With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (€STR) in Europe.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.

Suggested Citation

  • Calvia, Alessandro & De Donno, Marzia & Guardasoni, Chiara & Sanfelici, Simona, 2026. "Short-rate models with stochastic discontinuities: A PDE approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 129-156.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:129-156
    DOI: 10.1016/j.matcom.2026.04.034
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