论文标题
与交错边界方案和3（2）个Bogacki-Shampine Pairs的六阶紧凑型差异，用于定价自由边界选项
Sixth-Order Compact Differencing with Staggered Boundary Schemes and 3(2) Bogacki-Shampine Pairs for Pricing Free-Boundary Options
论文作者
论文摘要
我们提出了一个稳定的六阶紧凑型有限差异方案，具有动态的五阶交错边界方案，3（2）R-K Bogacki和洗发平的自适应时间踏上了定价美国风格的选择。要定位，以选项和三角洲灵敏度同时固定和计算自由边界，我们引入了Landau转换。此外，我们在定价模型中删除了对流术语，该术语可能会进一步引入错误。因此，可以轻松实施有效的六阶紧凑型方案。以离散形式耦合第六阶紧凑型方案的主要挑战是有效地说明了近规则的方案。在这项工作中，我们介绍了适用于解决模型的新型五阶和六阶近边界方案。使用从新颖的五阶交错边界方案获得的高阶分析近似来近似最佳的运动边界和其他边界值。此外，我们研究了从这个高阶分析近似获得的最佳运动边界的第一和第二个衍生物的平滑度。再加上3（2）个RK-Bogacki和洗发时间整合方法，然后使用第六阶紧凑型操作员近似内部值。获得了预期的收敛速率，我们目前的数值方案非常快，并且具有非常粗的网格的高度准确近似值。
We propose a stable sixth-order compact finite difference scheme with a dynamic fifth-order staggered boundary scheme and 3(2) R-K Bogacki and Shampine adaptive time stepping for pricing American style options. To locate, fix and compute the free-boundary simultaneously with option and delta sensitivity, we introduce a Landau transformation. Furthermore, we remove the convective term in the pricing model which could further introduce errors. Hence, an efficient sixth-order compact scheme can easily be implemented. The main challenge in coupling the sixth order compact scheme in discrete form is to efficiently account for the near-boundary scheme. In this work, we introduce novel fifth- and sixth-order Dirichlet near-boundary schemes suitable for solving our model. The optimal exercise boundary and other boundary values are approximated using a high-order analytical approximation obtained from a novel fifth-order staggered boundary scheme. Furthermore, we investigate the smoothness of the first and second derivatives of the optimal exercise boundary which is obtained from this high-order analytical approximation. Coupled with the 3(2) RK-Bogacki and Shampine time integration method, the interior values are then approximated using the sixth order compact operator. The expected convergence rate is obtained, and our present numerical scheme is very fast and gives highly accurate approximations with very coarse grids.
