CIR Models Can Jump on Scheduled Dates and Still Stay Affine

Overnight interest rates can spike on dates everyone already knows will matter, like central bank meetings. This paper shows how to build that behavior into a classic short-rate model without breaking its core structure. The authors extend the Cox-Ingersoll-Ross (CIR) process, a standard model for interest rates, by allowing jumps at predetermined dates called stochastic discontinuities. Each jump size depends on the rate just before the jump, so the model can move both up and down and can even create dependence between jumps. The paper proves that such a process exists under mild assumptions, and it identifies when the extended model still keeps the affine property of the original CIR process. It also gives examples that preserve both non-negativity and affinity, including one built by applying a deterministic cadlag time-change to a standard CIR process. Finally, the authors characterize when this richer CIR model is infinitely divisible, adding another piece to the affine modelling toolkit for overnight rates and other settings with scheduled jumps.

SOFR, the US overnight rate, can move in a straight line for days. Then a meeting date arrives, and the line can jump. That is awkward for old short-rate models. Those models were built for smooth motion. This article tackles that calendar-shaped problem. It asks how a classic CIR model can jump on known dates and still stay above zero. The goal is not drama for its own sake. The goal is a model that can handle spikes traders already expect. A model that misses those spikes will miss the story. That matters for money-market pricing and hedging. It also matters when the calendar itself changes the path. The curve needs to know when a meeting sits on the clock.

Why the old curve breaks on meeting days

The model adds jumps at fixed dates. Each jump size depends on the rate just before it. That choice matters. It lets the same setup jump up or down. It also lets one jump echo the last one. In plain words, the model can remember its recent past. The study proves that such a process exists under mild assumptions. It also gives exact conditions for keeping the affine property. That property is a math shape that keeps key formulas neat. The same examples also keep non-negativity, which means rates never fall below zero. The examples show both upward and downward jumps. So the calendar shock does not force one direction. That makes the model flexible enough for different meeting days. It keeps the main shape while changing the timing.

How a fixed clock makes the jumps

One route to the new model starts with a standard CIR process. That is a classic rate model that stays above zero. Then a fixed clock is laid over it. This time change is deterministic, so the jump times are known in advance. Between those dates, the path follows the old CIR logic. At each planned date, the jump size uses the level just before the jump. That ties each jump to the current state, not to a random outside shock. The same setup can keep the affine property. It can also keep non-negativity. The study shows when both survive together.

Why this matters for overnight rates

This matters because overnight rates are not just noisy. They can move on purpose. Central bank meetings can stamp those moves onto the calendar. A model that treats those jumps as random misses the point. This framework gives modellers a way to keep the rate above zero. It also lets them keep the neat affine form. That helps with pricing and hedging in this affine setting. The study also gives conditions for infinite divisibility. That means the process can be split into any number of matching pieces. In plain terms, the shape stays flexible without falling apart. That is useful when a market model must fit many dates at once.

What to test next

The next test is simple and specific. Fit the model to SOFR around central bank meeting dates. That is where the jump story should matter most. The hard check is whether one clock can fit calm days and jump days. It must do that without losing non-negativity. If it does, scheduled shocks stop looking like model errors. They become part of the design. That would make the old CIR curve feel less fragile. The surprise is that a classic shape can still absorb the calendar's jolts. That is the real promise of the extension.