CIR model (Cox-Ingersoll-Ross)
Quantitative Finance glossary · Quantitative Finance
Definition
Mean-reverting square-root short-rate model: dr_t = κ(θ - r_t),dt + σ√(r_t),dW_t. The √(r_t) diffusion makes the variance scale with the level, so rates stay non-negative under the Feller condition 2κθ ≥ σ^2 (which keeps the zero boundary unattainable). Closed-form zero-coupon bond price P(t,T) = A(t,T)e^-B(t,T)r_t (affine term structure). The variance dynamics are reused inside the Heston stochastic-vol model.
CIR model (Cox-Ingersoll-Ross) in plain English
Interest rates don't wander off to infinity or crash below zero forever — they tend to drift back toward some normal middle level, like a stretched rubber band snapping back. The CIR model is a formula that captures this 'pull toward normal' for short-term interest rates, where θ is the long-run level rates get tugged toward and κ is how strongly they're tugged. Its clever trick is the √(r_t) term: it makes rates jiggle less as they approach zero, so (under a simple condition) they never go negative — a realistic feature, since a rate of exactly zero is a natural floor. It's prized because it still gives a clean, exact formula for bond prices, and the same 'square-root' idea was later borrowed to model how stock-market volatility bounces around.
Also called: Cox-Ingersoll-Ross
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