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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.|
|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|
|Pages:||447 - 475|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Finance and Stochastics|
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