The Cox-Ingersoll-Ross (CIR) model is a mathematical model used to describe the dynamics of interest rates. It is part of the class of affine term structure models and is particularly known for its ability to capture the behavior of interest rates in a way that ensures non-negative rates. The CIR model was introduced by economists David Cox, Jonathan Ingersoll, and Stephen Ross in the early 1980s.
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A nonnegative mean-reverting short-rate diffusion with positive parameters. Its mean-reversion level is and its diffusion size is proportional to . The Feller positivity condition for the CIR model controls whether zero is reachable. Its stationary law is a gamma distribution and its zero-coupon bond prices are exponential-affine.