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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.