Duality and convergence for binomial markets with friction

Yan Dolinsky; Halil Mete Soner

doi:10.1007/s00780-012-0192-1

Duality and convergence for binomial markets with friction

Yan Dolinsky^*, Halil Mete Soner

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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
Pages (from-to)	447-475
Number of pages	29
Journal	Finance and Stochastics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s00780-012-0192-1
State	Published - Jul 2013
Externally published	Yes

Bibliographical note

Funding Information:
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.

Keywords

Binomial model
G-Expectation
Limit theorems
Liquidity
Super-replication

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10.1007/s00780-012-0192-1

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title = "Duality and convergence for binomial markets with friction",

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 {\c C}etin et al. (Finance Stoch. 8:311-341, 2004) is proved. Hence, this paper extends the previous convergence result of G{\"o}kay 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 = "Binomial model, G-Expectation, Limit theorems, Liquidity, Super-replication",

author = "Yan Dolinsky and Soner, {Halil Mete}",

note = "Funding Information: 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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AU - Dolinsky, Yan

AU - Soner, Halil Mete

N1 - Funding Information: 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.

PY - 2013/7

Y1 - 2013/7

N2 - 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).

AB - 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).

KW - Binomial model

KW - G-Expectation

KW - Limit theorems

KW - Liquidity

KW - Super-replication

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IS - 3

ER -

Duality and convergence for binomial markets with friction

Abstract

Bibliographical note

Keywords

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