Technology Category
Search and Optimization: Mixed Discrete/Continuous SearchReasoning under Uncertainty: Stochastic OptimizationConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
Short-rate models with stochastic discontinuities: a PDE approach
🤖 AI Summary
Following the reform of interest rate benchmarks, risk-free rates such as SOFR and €STR exhibit discontinuous jumps and spikes at fixed time points—driven by regulatory interventions and liquidity shocks—rendering conventional continuous-time models inadequate. To address this, we propose a novel class of short-rate models incorporating random-magnitude discontinuities at predetermined times. We establish, for the first time, a Feynman–Kac partial differential equation (PDE) representation tailored to such jump structures and derive quasi-analytic solutions for affine discontinuous models. Furthermore, integrating stochastic process theory with robust PDE numerical methods, we design a general-purpose, numerically stable pricing algorithm. Our framework significantly improves both modeling accuracy and computational efficiency for RFR-linked derivatives—including futures and swaptions—and demonstrates robustness and practicality across multiple market regimes.
Technology Category
Application Category
📝 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With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (euro STR) in Europe.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.
Problem
Research questions and friction points this paper is trying to address.
Modeling interest rate jumps and spikes in benchmark reforms
Developing PDE methods for pricing derivatives with discontinuities
Providing analytical and numerical solutions for affine models
Innovation
Methods, ideas, or system contributions that make the work stand out.
Short-rate model with stochastic discontinuities at fixed times
PDE-based approach for pricing interest rate derivatives
Closed-form solutions for affine models and numerical methods
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