Embedding the Vasicek model into the Cox-Ingersoll-Ross model

The Cox-Ingersoll-Ross (CIR) model and the Vasicek model are two well-known single factor models of the interest spot rate. In this paper, we construct a mapping by means of which the price of a zero-coupon bond in the CIR model may be obtained from a corresponding price in the Vasicek model. We use symmetry analysis to construct this mapping and verify it by transforming three arbitrary solutions of the pricing equation in the Vasicek model into solutions of the corresponding equation in the CIR model. © 2010 John Wiley & Sons, Ltd