Short-rate models with stochastic discontinuities: a PDE approach

Paper: arXiv 2510.04289

Authors: Alessandro Calvia, Marzia De Donno, Chiara Guardasoni, Simona Sanfelici

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With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR) in Europe.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

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical treatment of short-rate models with stochastic discontinuities using a PDE framework and Feynman-Kač representations. However, it is primarily theoretical and lacks empirical backtesting or real-world data validation on post-LIBOR RFR rates.

Research Flowchart

  flowchart TD
    A[Research Goal: Price interest rate derivatives under RFR jumps/spikes] --> B[Data Inputs: RFR Characteristics & Market Events e.g., SOFR, €STR]
    B --> C[Formulate Short-Rate Model with Discontinuities at Fixed Times]
    C --> D[Establish PDE Framework & Feynman-Kac Representation]
    D --> E{Model Type Branching}
    E -->|Affine Models| F[Derive Analytical Quasi Closed-Form Solutions]
    E -->|General Models| G[Develop PDE Numerical Solvers]
    F --> H[Key Outcome: Accurate Derivative Pricing post-IBOR Transition]
    G --> H