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Binomial approximations of shortfall risk for game options

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  • Yan Dolinsky
  • Yuri Kifer

Abstract

We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and continuous-time cases. These results are new also for usual American style options. The paper continues and extends the study of Kifer [Ann. Appl. Probab. 16 (2006) 984--1033] where estimates for binomial approximations of prices of game options were obtained. Our arguments rely, in particular, on strong invariance principle type approximations via the Skorokhod embedding, estimates from Kifer [Ann. Appl. Probab. 16 (2006) 984--1033] and the existence of optimal shortfall hedging in the discrete time established by Dolinsky and Kifer [Stochastics 79 (2007) 169--195].

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  • Yan Dolinsky & Yuri Kifer, 2008. "Binomial approximations of shortfall risk for game options," Papers 0811.1896, arXiv.org.
    • Handle: RePEc:arx:papers:0811.1896
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    References listed on IDEAS

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    1. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
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    Cited by:

    1. Yan Dolinsky, 2010. "Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Model," Papers 1004.1574, arXiv.org.
    2. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
    3. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    4. Yan Dolinsky & Yuri Kifer, 2009. "Binomial Approximations for Barrier Options of Israeli Style," Papers 0907.4136, arXiv.org.

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