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By Mengmeng Ma, Student Id, The Cox and Ross Model

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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Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.416.2387
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