Duality and convergence for binomial markets with friction
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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).
KeywordsSuper-replication Liquidity Binomial model Limit theorems G-Expectation
Mathematics Subject Classification (2010)91G10 60F05 60H30
JEL ClassificationG11 G13 D52
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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