Wiener chaos and the Cox–Ingersoll–Ross model

Abstract

In this paper we recast the Cox–Ingersoll–Ross (CIR) 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 n th 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.