A Fast Numerical Method for the Black-Scholes Equation of American Options

Houde Han, Xiaonan Wu

Research output: Contribution to journalJournal articlepeer-review

78 Citations (Scopus)
79 Downloads (Pure)


This paper introduces a fast numerical method for computing American option pricing problems governed by the Black-Scholes equation. The treatment of the free boundary is based on some properties of the solution of the Black-Scholes equation. An artificial boundary condition is also used at the other end of the domain. The finite difference method is used to solve the resulting problem. Computational results are given for some American call option problems. The results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method.

Original languageEnglish
Pages (from-to)2081-2095
Number of pages15
JournalSIAM Journal on Numerical Analysis
Issue number6
Publication statusPublished - Nov 2003

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • American option
  • Artificial boundary condition
  • Finite difference method
  • Free boundary


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