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).
Original language | English (US) |
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Pages (from-to) | 447-475 |
Number of pages | 29 |
Journal | Finance and Stochastics |
Volume | 17 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2013 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Finance
- Statistics, Probability and Uncertainty
Keywords
- Binomial model
- G-Expectation
- Limit theorems
- Liquidity
- Super-replication