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Duality and convergence for binomial markets with friction

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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).

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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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Authors and Affiliations

  1. Dept. of Mathematics, ETH Zurich, Zurich, Switzerland

    Yan Dolinsky & Halil Mete Soner

  2. Swiss Finance Institute, Zurich, Switzerland

    Halil Mete Soner

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  1. Yan Dolinsky
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  2. Halil Mete Soner
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Correspondence to Yan Dolinsky.

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Dolinsky, Y., Soner, H.M. Duality and convergence for binomial markets with friction. Finance Stoch 17, 447–475 (2013). https://doi.org/10.1007/s00780-012-0192-1

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  • DOI: https://doi.org/10.1007/s00780-012-0192-1

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