Wiener chaos and the Cox–Ingersoll–Ross model
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In this we 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 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.
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