The Wiener chaos expansion for the Cox–Ingersoll–Ross model

In this paper we recast the Cox–Ingersoll–Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning 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. ∗Research supported by the Natural Sciences and Engineering Research Council of Canada and Mathematics of Information Technology and Complex Systems, Canada