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Duality and Convergence for Binomial Markets with Friction

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  • Yan Dolinsky
  • Halil Mete Soner
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    Abstract

    We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the super-replication cost in these models are obtained and used to prove the limit theorems. In particular, the existence of the liquidity premium for the continuous time limit of the model proposed in [6] is proved. Hence, this paper extends the previous convergence result of [13] to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the $G$-expectation of Peng as earlier proved by Kusuoka in [14].

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    File URL: http://arxiv.org/pdf/1106.2095
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    Paper provided by arXiv.org in its series Papers with number 1106.2095.

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    Date of creation: Jun 2011
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    Handle: RePEc:arx:papers:1106.2095

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    1. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    2. Umut Cetin & L.C.G. Rogers, 2007. "Modeling liquidity effects in discrete time," LSE Research Online Documents on Economics 2844, London School of Economics and Political Science, LSE Library.
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    Cited by:
    1. Christian Bayer & Bezirgen Veliyev, 2012. "Utility Maximization in a Binomial Model with transaction costs: a Duality Approach Based on the Shadow Price Process," Papers 1209.5175, arXiv.org.

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