Error estimates for binomial approximations of game options

Details Error estimates for binomial approximations of game options Error estimates for binomial approximations of game options

2006-07-05

arxiv.org/abs/math/0607123v1

Annals of Applied Probability 2006, Vol. 16, No. 2, 984-1033

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000088 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000088

We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomial approximations yield for game options in the Black--Scholes market ``nearly'' rational exercise times and ``nearly'' hedging self-financing portfolios with small average shortfalls and initial capitals close to fair prices of the options. The estimates rely on strong invariance principle type approximations via the Skorokhod embedding.

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