Wiener chaos and the Cox–Ingersoll–Ross model
Wiener chaos and the Cox–Ingersoll–Ross model
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DOI：
10.1098/rspa.2004.1366
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发表时间：
2003-07
期刊：
影响因子：
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通讯作者：
M. Grasselli;T. Hurd
中科院分区：
文献类型：
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作者：
M. Grasselli;T. Hurd
在本文中，我们将Cox-Ingersoll-Ross （CIR）利率模型转换为最近由Hughston和Rafailidis引入的混沌表示。从CIR模型的“高斯平方表示”开始，我们找到了基本随机变量X∞的简单表达式。利用无限维高斯积分理论的技术，我们导出了CIR模型的Wiener混沌展开的第n项的显式公式，对于n = 0,1,2,....然后，我们推导了零息债券价格的新表达式，它揭示了高斯测度与Ricatti微分方程之间的联系。
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 nth 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.