On the early exercise boundary of the American put option

Jonathan Goodman, Daniel N. Ostrov

Research output: Contribution to journalArticlepeer-review


We study the short time behavior of the early exercise boundary for American style put options in the Black Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integral equation is derived from the time derivative of the option value function, which closely resembles the classical Stefan free boundary value problem for melting ice. Our analytical results are supported by numerical computations designed for very short times.

Original languageEnglish (US)
Pages (from-to)1823-1838
Number of pages16
JournalSIAM Journal on Applied Mathematics
Issue number5
StatePublished - May 2002


  • American put
  • Black-Scholes
  • Free boundary

ASJC Scopus subject areas

  • Applied Mathematics


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