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Duality and convergence for binomial markets with friction

Author(s): Dolinsky, Y; Soner, H Mete

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Abstract: We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin et al. (Finance Stoch. 8:311-341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250-276, 2012) 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 (Ann. Appl. Probab. 5:198-221, 1995). © 2012 Springer-Verlag.
Publication Date: 1-Jul-2013
Citation: Dolinsky, Y, Soner, HM. (2013). Duality and convergence for binomial markets with friction. Finance and Stochastics, 17 (3), 447 - 475. doi:10.1007/s00780-012-0192-1
DOI: doi:10.1007/s00780-012-0192-1
ISSN: 0949-2984
Pages: 447 - 475
Type of Material: Journal Article
Journal/Proceeding Title: Finance and Stochastics
Version: Author's manuscript

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