The black-scholes equation revisited: Asymptotic expansions and singular perturbations

Martin Widdicks, Peter W. Duck, Ari D. Andricopoulos, David P. Newton

Research output: Contribution to journalArticlepeer-review


In this paper, novel singular perturbation techniques are applied to price European, American, and barrier options. Employment of these methods leads to a significant simplification of the problem in all cases, by reducing the number of parameters. For American options, the valuation problem is reduced to a procedure that may be performed on a rudimentary handheld calculator. The method also sheds light on the evolution of option prices for all of the cases considered, the results being particularly illuminating for American and barrier options.

Original languageEnglish (US)
Pages (from-to)373-391
Number of pages19
JournalMathematical Finance
Issue number2
StatePublished - Apr 2005
Externally publishedYes


  • Look-up tables
  • Numerical techniques
  • Option valuation
  • Singular perturbation theory

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics


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