采用高阶紧凑格式和自适应时间步进,提高了求解美国CEV模型的精度

Chinonso Nwankwo, Weizhong Dai, Tony Ware
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引用次数: 0

摘要

在本研究中,我们提出了一种高阶时间适应方案,用于等距和局部精细空间网格上固定自由边界不变弹性方差(CEV)模型耦合系统的定价。我们的方法大大提高了性能,改善了模型中固有和诱导的不规则性。此外,耦合偏微分方程系统是强非线性的,涉及多个时间相关系数,其中包括早期运动边界的一阶导数。这些系数是从使用正则平方根函数导出的四阶解析近似中近似出来的。在非一致的四阶紧致有限差分格式下,得到了选择值和灵敏度的半离散方程。采用五阶5(4)Dormand-Prince时间积分法求解离散方程耦合系统。通过局部网格细化和自适应策略增强我们提出的方法的性能,使我们能够在非常粗糙的空间网格中获得高度精确的分辨率,从而大大减少了计算运行时间。我们进一步验证了我们的方法的性能,并与一些知名的和性能更好的现有方法进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our method is substantially enhanced to improve irregularities in the model which are both inherent and induced. Furthermore, the system of coupled PDEs is strongly nonlinear and involves several time-dependent coefficients that include the first-order derivative of the early exercise boundary. These coefficients are approximated from a fourth-order analytical approximation which is derived using a regularized square-root function. The semi-discrete equation for the option value and delta sensitivity is obtained from a non-uniform fourth-order compact finite difference scheme. Fifth-order 5(4) Dormand-Prince time integration method is used to solve the coupled system of discrete equations. Enhancing the performance of our proposed method with local mesh refinement and adaptive strategies enables us to obtain highly accurate solution with very coarse space grids, hence reducing computational runtime substantially. We further verify the performance of our methodology as compared with some of the well-known and better-performing existing methods.
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