Binomial approximations for barrier options of Israeli style

Yan Dolinsky*, Yuri Kifer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

3 Scopus citations

Abstract

We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black–Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market with path dependent payoffs and we estimate the speed of convergence. The results are also new for usual American style options and they are interesting from a computational point of view, since in binomial markets these quantities can be obtained via dynamic programming algorithms. The paper extends [6] and [3] but requires substantial additional arguments in view of peculiarities of barrier options which, in particular, destroy the regularity of payoffs needed in the above papers.

Original languageAmerican English
Title of host publicationAnnals of the International Society of Dynamic Games
PublisherBirkhauser
Pages447-467
Number of pages21
DOIs
StatePublished - 2011

Publication series

NameAnnals of the International Society of Dynamic Games
Volume11
ISSN (Print)2474-0179
ISSN (Electronic)2474-0187

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media, LLC 2011.

Keywords

  • Barrier option
  • Initial capital
  • Open interval
  • Option price
  • Stock price

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