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Wiener Chaos and the Cox-Ingersoll-Ross model

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  • M. R. Grasselli
  • T. R. Hurd
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    Abstract

    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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    File URL: http://arxiv.org/pdf/math/0307197
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0307197.

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    Date of creation: Jul 2003
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    Publication status: Published in Proc. R. Soc. A (2005) 461, 459\^A?"479
    Handle: RePEc:arx:papers:math/0307197

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    Web page: http://arxiv.org/

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    Cited by:
    1. Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Papers 0910.5033, arXiv.org.

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