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Abstract

The CIR model is an equilibrium asset pricing model for the term structure of interest rate. It is defined under the assumption: dr t = k( θ − r) dt + σ t r dZt t where k, θ, σ are constants. k represents the rates of mean reversion, θ represents the long 2 2 run average. Assuming 2kθ ≥ σ, then the interest rate is ensured to be positive ( 2kθ < σ, it is possible for r to reach zero instantaneously, but it will never become negative). Under the equivalent risk-neutral measure, it be comes dr t = ( kθ − ( k + λ) r) dt + σ t r dZt t where λ represents the risk adjustments when moving to the risk-neutral distribution. The CIR model is affine, and has a non-central chi-squared distribution (with degree of 4k freedom v

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