Binomial approximations for barrier options of Israeli style

Yan Dolinsky; Yuri Kifer

doi:10.1007/978-0-8176-8089-3_22

Binomial approximations for barrier options of Israeli style

Yan Dolinsky^*, Yuri Kifer

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-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 language	English
Title of host publication	Annals of the International Society of Dynamic Games
Publisher	Birkhauser
Pages	447-467
Number of pages	21
DOIs	https://doi.org/10.1007/978-0-8176-8089-3_22
State	Published - 2011

Publication series

Name	Annals of the International Society of Dynamic Games
Volume	11
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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10.1007/978-0-8176-8089-3_22

Cite this

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AB - 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.

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KW - Initial capital

KW - Open interval

KW - Option price

KW - Stock price

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ER -

Binomial approximations for barrier options of Israeli style

Abstract

Publication series

Bibliographical note

Keywords

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