Duality and convergence for binomial markets with friction |
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Authors: | Yan Dolinsky Halil Mete Soner |
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Institution: | 1. Dept. of Mathematics, ETH Zurich, Zurich, Switzerland 2. Swiss Finance Institute, Zurich, Switzerland
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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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