CIR model (Cox-Ingersoll-Ross)

Quantitative Finance Glossary

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.

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