Robust hedging with proportional transaction costs

Yan Dolinsky; H. Mete Soner

doi:10.1007/s00780-014-0227-x

Robust hedging with proportional transaction costs

Yan Dolinsky, H. Mete Soner

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

50 Scopus citations

Abstract

A duality for robust hedging with proportional transaction costs of pathdependent European options is obtained in a discrete-time financial market with one risky asset. The investor's portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge-Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.

Original language	English (US)
Pages (from-to)	327-347
Number of pages	21
Journal	Finance and Stochastics
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s00780-014-0227-x
State	Published - Apr 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Finance
Statistics, Probability and Uncertainty

Keywords

Consistent price systems
European options
Fundamental theorem of asset pricing
Optimal transport
Robust hedging
Superreplication
Transaction costs
Weak convergence

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10.1007/s00780-014-0227-x

Cite this

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title = "Robust hedging with proportional transaction costs",

abstract = "A duality for robust hedging with proportional transaction costs of pathdependent European options is obtained in a discrete-time financial market with one risky asset. The investor's portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge-Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.",

keywords = "Consistent price systems, European options, Fundamental theorem of asset pricing, Optimal transport, Robust hedging, Superreplication, Transaction costs, Weak convergence",

author = "Yan Dolinsky and Soner, {H. Mete}",

note = "Funding Information: Research of Dolinsky is partly supported by a career integration grant, CIG- 618235 and research of Soner is supported by the European Research Council under the grant 228053-FiRM, by the ETH Foundation, and by the Swiss Finance Institute. The authors would like to thank Lev Buhovsky, Jan Ob{\l}{\'o}j, and Josef Teichmann for insightful discussions and comments.",

year = "2014",

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doi = "10.1007/s00780-014-0227-x",

language = "English (US)",

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AU - Dolinsky, Yan

AU - Soner, H. Mete

N1 - Funding Information: Research of Dolinsky is partly supported by a career integration grant, CIG- 618235 and research of Soner is supported by the European Research Council under the grant 228053-FiRM, by the ETH Foundation, and by the Swiss Finance Institute. The authors would like to thank Lev Buhovsky, Jan Obłój, and Josef Teichmann for insightful discussions and comments.

PY - 2014/4

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N2 - A duality for robust hedging with proportional transaction costs of pathdependent European options is obtained in a discrete-time financial market with one risky asset. The investor's portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge-Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.

AB - A duality for robust hedging with proportional transaction costs of pathdependent European options is obtained in a discrete-time financial market with one risky asset. The investor's portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge-Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.

KW - Consistent price systems

KW - European options

KW - Fundamental theorem of asset pricing

KW - Optimal transport

KW - Robust hedging

KW - Superreplication

KW - Transaction costs

KW - Weak convergence

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Robust hedging with proportional transaction costs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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