The Annals of Applied Probability

Error estimates for binomial approximations of game options

Yuri Kifer

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 2 (2006), 984-1033.

Dates
First available in Project Euclid: 29 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1151592257

Digital Object Identifier
doi:10.1214/105051606000000088

Mathematical Reviews number (MathSciNet)
MR2244439

Zentralblatt MATH identifier
1142.91533

Subjects
Primary: 91B28
Secondary: 60F15: Strong theorems 91A05: 2-person games

Keywords
Game options Dynkin games complete markets binomial approximation Skorokhod embedding

Citation

Kifer, Yuri. Error estimates for binomial approximations of game options. Ann. Appl. Probab. 16 (2006), no. 2, 984--1033. doi:10.1214/105051606000000088. https://projecteuclid.org/euclid.aoap/1151592257


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