Black-Scholes和Heston方程围道积分方法的评价
Appraisal of a contour integral method for the Black-Scholes and Heston equations
摘要：
Weideman [IMA J. Numer.肛门，出现]的积分半离散对流扩散偏微分方程，推广应用到金融数学的一些重要方程。使用空间算子的数值范围的估计，最佳轮廓参数的理论推导和数值测试。测试示例是布莱克-斯科尔斯偏微分方程在一个空间维度和赫斯顿偏微分方程在两个维度。在后者的情况下，效率相比，ADI分裂计划解决这个问题。在例子中，它被发现，轮廓积分方法是优越的范围内的中等到高精度的要求。对目前的围道积分方法的实现提出了进一步的改进建议。
英文摘要：
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parameters are derived theoretically and tested numerically. Test examples presented are the Black-Scholes PDE in one space dimension and the Heston PDE in two dimensions. In the latter case efficiency is compared to ADI splitting schemes for solving this problem. In the examples it is found that the contour integral method is superior for the range of medium to high accuracy requirements. Further improvements to the current implementation of the contour integral method are suggested.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
