Wiener chaos and the Cox-Ingersoll-Ross model

In this paper we recast the Cox–Ingersoll–Ross (CIR) model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Begin-ning with the ‘squared Gaussian representation ’ of the CIR model, we find a simple expression for the fundamental random variable X∞. By use of techniques from the theory of infinite-dimensional Gaussian integration, we derive an explicit formula for the nth term of the Wiener chaos expansion of the CIR model, for n = 0, 1, 2,.... We then derive a new expression for the price of a zero coupon bond which reveals a connection between Gaussian measures and Ricatti differential equations