Duality and convergence for binomial markets with friction

Yan Dolinsky () and Halil Soner ()

Finance and Stochastics, 2013, vol. 17, issue 3, 447-475

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 ). Copyright Springer-Verlag 2013

Keywords: Super-replication; Liquidity; Binomial model; Limit theorems; G-Expectation; 91G10; 60F05; 60H30; G11; G13; D52 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (16)

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DOI: 10.1007/s00780-012-0192-1

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