Derivation of probability density function of CIR model under a specific condition

Abstract

In economics and finance, the Cox–Ingersoll–Ross model (or CIR model) is being generally used to model the interest rates. The CIR model is an extension of the Vasicek model and it ensures a mean reversion of the interest rates and it avoids the possibility of negative interest rates. In this work, an explicit formula for probability density function of CIR model has been derived and the final formula comport well when interest rate is close to zero.