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Error estimates for binomial approximations of game options. (English) Zbl 1142.91533

Ann. Appl. Probab. 16, No. 2, 984-1033 (2006); correction ibid. 18, No. 3, 1271-1277 (2008).
Summary: 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60F15 Strong limit theorems
91A05 2-person games
91A15 Stochastic games, stochastic differential games
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References:

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