Finance and Stochastics

, Volume 17, Issue 3, pp 447–475 | Cite as

Duality and convergence for binomial markets with friction

Article

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).

Keywords

Super-replication Liquidity Binomial model Limit theorems G-Expectation 

Mathematics Subject Classification (2010)

91G10 60F05 60H30 

JEL Classification

G11 G13 D52 

Notes

Acknowledgements

Research supported by the European Research Council Grant 228053-FiRM, the Swiss Finance Institute and the ETH Foundation. The authors would like to thank Prof. Kusuoka and Marcel Nutz for insightful discussions.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Dept. of MathematicsETH ZurichZurichSwitzerland
  2. 2.Swiss Finance InstituteZurichSwitzerland

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