Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model

We propose an empirical method that utilizes the conditional density of the state variables to estimate and test a term structure model with known price formulae, using data on both discount and coupon bonds. The method is applied to an extension of a two‐factor model due to Cox, Ingersoll, and Ross (1985 ; CIR). Our results show that estimates based on only bills imply unreasonably large price errors for longer maturities. We reject the original CIR model using a likelihood ratio test, and conclude that the extended CIR model also fails to provide a good description of the Treasury market.