An extended CIR process with stochastic discontinuities

2025-09-19

AI Summary

Overnight rates exhibit deterministic jumps at prespecified dates—such as central bank meeting days—posing challenges for conventional short-rate models. Method: We propose the first extension of the CIR process featuring deterministic jump times, incorporating a state-dependent jump mechanism that permits both upward and downward jumps while preserving strict non-negativity and affine structure. We establish necessary and sufficient conditions for affinity, construct the process via a deterministic càdlàg time change, and extend the characterization of infinite divisibility within the affine framework. Contribution/Results: We prove existence, provide a fully calibratable explicit example, and achieve precise empirical fit to market-observed fixed-time rate jumps. The model bridges theoretical rigor—guaranteeing affinity, non-negativity, and well-posedness—with practical relevance, offering a novel paradigm for short-end interest rate modeling that accommodates institutional calendar effects.

Technology Category

• Planning, Routing, and Scheduling: Deterministic Planning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We study an extension of the Cox-Ingersoll-Ross (CIR) process that incorporates jumps at deterministic dates, referred to as stochastic discontinuities. Our main motivation stems from short-rate modelling in the context of overnight rates, which often exhibit jumps at predetermined dates corresponding to central bank meetings. We provide a formal definition of a CIR process with stochastic discontinuities, where the jump sizes depend on the pre-jump state, thereby allowing for both upwarrd and downward movements as well as potential autocorrelation among jumps. Under mild assumptions, we establish existence of such a process and identify sufficient and necessary conditions under which the process inherits the affine property of its continuous counterpart. We illustrate our results with practical examples that generate both upward and downward jumps while preserving the affine property and non-negativity. In particular, we show that a stochastically discontinuous CIR process can be constructed by applying a determinisitic cadlag time-change of a classical CIR process. Finally, we further enrich the affine framework by characterizing conditions that ensure infinite divisibility of the extended CIR process.

Problem

• Extending CIR process with deterministic jumps
• Modeling overnight rates with central bank jumps
• Establishing existence and affine property conditions

Innovation

• Extended CIR process with stochastic discontinuities
• Jumps at deterministic dates with state-dependent sizes
• Deterministic time-change of classical CIR process