Convergence of the mimetic finite difference and fitted mimetic finite difference method for options pricing

作者：

Highlights：

• Two novel numerical based on the mimetic finite difference method for a degenerated Black Scholes PDE are considered.

• The degeneracy of the PDE, is handled using the fitted technique.

• Rigorous convergence proofs in appropriate normed spaces are investigated.

• Theoretical results are validated with numerical simulations and the robustness of the schemes are investigated.

摘要

•Two novel numerical based on the mimetic finite difference method for a degenerated Black Scholes PDE are considered.•The degeneracy of the PDE, is handled using the fitted technique.•Rigorous convergence proofs in appropriate normed spaces are investigated.•Theoretical results are validated with numerical simulations and the robustness of the schemes are investigated.

论文关键词：Option pricing,Black-Scholes equation,Mimetic finite difference method,Implicit scheme

论文评审过程：Received 3 January 2020, Revised 25 January 2021, Accepted 31 January 2021, Available online 24 February 2021, Version of Record 24 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126060