High order discretization schemes for the CIR process: Application to affine term structure and Heston models
High order discretization schemes for the CIR process: Application to affine term structure and Heston models
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DOI：
10.1090/s0025-5718-09-02252-2
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Alfonsi
中科院分区：
文献类型：
--
作者：
A. Alfonsi
本文给出了Cox-Ingersoll-Ross （CIR）过程的弱二阶格式和弱三阶格式，对其参数没有任何限制。同时，在Ninomiya和Victoir \cite{NV}的基础上，给出了得到弱二阶格式的一般递归构造方法。结合这两个结果，这允许提出更一般的仿射扩散的二阶格式。仿真实例说明了这些方案在CIR模型和Heston模型上的收敛性。算法是用伪代码语言表述的。
This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process, without any restriction on its parameters. At the same time, it gives a general recursive construction method to get weak second-order schemes that extends the one introduced by Ninomiya and Victoir~\cite{NV}. Combining these both results, this allows to propose a second-order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models. Algorithms are stated in a pseudocode language.