论文标题
一种自适应和明确的第四阶runge-kutta-fehlberg方法，加上紧凑的有限差异，以定价美国pot选项
An Adaptive and Explicit Fourth Order Runge-Kutta-Fehlberg Method Coupled with Compact Finite Differencing for Pricing American Put Options
论文作者
论文摘要
我们提出了一种自适应和显式的四阶Runge-kutta-fehlberg方法，并结合了四阶紧凑型方案，以解决美国的PUT期权问题。首先，通过对数转换并采用其他衍生物，将自由边界问题转换为具有固定域的部分微分方程系统。通过添加具有固定自由边界的中间函数，得出了二次公式以分析最佳运动边界的速度。此外，我们实施了一种外推方法，以确保至少在计算从其导数中计算最佳锻炼边界时，在边界点保持空间的三阶精度。因此，它使我们能够使用Dirichlet边界条件使用四阶空间和时间离散化，以获得资产选项，选项Greeks和最佳运动边界的数值解决方案。 runge-kutta-fehlberg方法的优点基于误差控制和调整时间步，以将误差保持在一定阈值。通过与数值实验中的一些现有方法进行比较，它表明该方法在计算速度方面具有更好的性能，并提供了更准确的解决方案。
We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial differential equations with a fixed domain by using logarithm transformation and taking additional derivatives. With the addition of an intermediate function with a fixed free boundary, a quadratic formula is derived to compute the velocity of the optimal exercise boundary analytically. Furthermore, we implement an extrapolation method to ensure that at least, a third-order accuracy in space is maintained at the boundary point when computing the optimal exercise boundary from its derivative. As such, it enables us to employ fourth-order spatial and temporal discretization with Dirichlet boundary conditions for obtaining the numerical solution of the asset option, option Greeks, and the optimal exercise boundary. The advantage of the Runge-Kutta-Fehlberg method is based on error control and the adjustment of the time step to maintain the error at a certain threshold. By comparing with some existing methods in the numerical experiment, it shows that the present method has a better performance in terms of computational speed and provides a more accurate solution.
