(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.