论文标题
在有限差异化中插入或伸展点
Inserting or Stretching Points in Finite Difference Discretizations
论文作者
论文摘要
部分微分方程有时会在解决方案或某些衍生物不连续的情况下具有关键点。最简单的示例是在初始条件下的不连续性。众所周知，那些降低了有限差异方法的准确性。一种常见的补救措施是拉伸网格，使得临界点附近存在更多的网格点，而在溶液则被视为光滑的地方更少。另一种解决方案是插入点，使得不连续性落在两个网格点的中间。本文比较了在黑色 - choles模型中金融衍生合同的定价中两种方法的准确性，并提出了一种新的快速和简单的拉伸功能。
Partial differential equations sometimes have critical points where the solution or some of its derivatives are discontinuous. The simplest example is a discontinuity in the initial condition. It is well known that those decrease the accuracy of finite difference methods. A common remedy is to stretch the grid, such that many more grid points are present near the critical points, and fewer where the solution is deemed smooth. An alternative solution is to insert points such that the discontinuities fall in the middle of two grid points. This paper compares the accuracy of both approaches in the context of the pricing of financial derivative contracts in the Black-Scholes model and proposes a new fast and simple stretching function.
