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Binomial Approximations for Barrier Options of Israeli Style

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  • Yan Dolinsky
  • Yuri Kifer
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    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 the speed of convergence is estimated, as well. The results are new also for usual American style options and they are interesting from the computational point of view, as well, since in binomial markets these quantities can be obtained via dynamical programming algorithms. The paper continues the study of [11]and [7] but requires substantial additional arguments in view of pecularities of barrier options which, in particular, destroy the regularity of payoffs needed in the above papers.

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    File URL: http://arxiv.org/pdf/0907.4136
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    Paper provided by arXiv.org in its series Papers with number 0907.4136.

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    Date of creation: Jul 2009
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    Handle: RePEc:arx:papers:0907.4136

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    1. L.C.G. Rogers & E.J. Stapleton, 1997. "Fast accurate binomial pricing," Finance and Stochastics, Springer, vol. 2(1), pages 3-17.
    2. Yan Dolinsky & Yuri Kifer, 2008. "Binomial approximations of shortfall risk for game options," Papers 0811.1896, arXiv.org.
    3. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
    4. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double-Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378.
    5. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
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