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 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  and  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.
KeywordsStock Price Option Price Open Interval Initial Capital Barrier Option
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