Sixth-Order Compact Differencing with Staggered Boundary Schemes and 3(2) Bogacki-Shampine Pairs for Pricing Free-Boundary Options

@article{Nwankwo2022SixthOrderCD,
  title={Sixth-Order Compact Differencing with Staggered Boundary Schemes and 3(2) Bogacki-Shampine Pairs for Pricing Free-Boundary Options},
  author={Chinonso Nwankwo and Weizhong Dai},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.14379}
}
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… 

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