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