英文标题：
《Approximating explicitly the mean reverting CEV process》
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作者：
Nikolaos Halidias and Ioannis Stamatiou
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最新提交年份：
2015
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英文摘要：
  In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations with sub-linear diffusion coefficients of the form $(x_t)^q,$ where $\\frac{1}{2}<q<1.$ Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameter $q.$ Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the whole two-dimensional stochastic volatility model, with instantaneous variance process given by the above mean reverting CEV process.
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中文摘要：
在本文中，我们希望进一步利用Halidias和Stamatiou（2015）提出的半离散方法。我们对金融数学模型中出现的均值回复CEV过程的数值解感兴趣，这些过程被描述为具有形式为$（x_t）^q$的亚线性扩散系数的某些随机微分方程的非负解，其中$\\frac{1}{2}<q<1.$我们的目标是构造保持正性的显式数值格式。我们证明了所提出的SD格式的收敛性，速度取决于参数$q。$此外，我们通过数值实验验证了我们的发现，并与其他保正格式进行了比较。最后，我们展示了如何处理整个二维随机波动率模型，其中瞬时方差过程由上述均值回复CEV过程给出。
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分类信息：

一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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