The Wiener Chaos Expansion for the CIR Model
Professor Matheus Grasselli, Department of Mathematics, McMaster University, Ontario
(Joint work with Professor T.R. Hurd, McMaster University.)

Abstract:
We recast the Cox-Ingersoll-Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. From the squared Gaussian formulation of the CIR model, we find a simple expression for the fundamental random variable X underlying the chaotic approach and prove that it is square integrable. Using techniques from infinite dimensional Gaussian integration, we then derive an explicit formula for the n-th term of the Wiener chaos expansion of the CIR model. Finally we derive a new expression for the price of a zero coupon bond which reveals a connection between Gaussian measures and Ricatti differential equations.