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Martingale transport with homogeneous stock movements

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  • Stephan Eckstein
  • Michael Kupper

Abstract

We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds on a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption, which restricts the variability of the forward-looking transitions of the martingale across time. We provide a dual formulation in terms of superhedging and discuss relaxations of the time-homogeneity assumption by adding market frictions. In financial terms, the introduced time-homogeneity corresponds to a time-consistency condition for call prices, given the state of the stock. The time homogeneity assumption leads to improved price bounds since market data from many time points can be incorporated effectively. The approach is illustrated with two numerical examples.

Suggested Citation

  • Stephan Eckstein & Michael Kupper, 2021. "Martingale transport with homogeneous stock movements," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 271-280, February.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:2:p:271-280
    DOI: 10.1080/14697688.2020.1787493
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    Cited by:

    1. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    2. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    3. Sester, Julian, 2024. "A multi-marginal c-convex duality theorem for martingale optimal transport," Statistics & Probability Letters, Elsevier, vol. 210(C).
    4. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    5. Ariel Neufeld & Julian Sester, 2021. "A deep learning approach to data-driven model-free pricing and to martingale optimal transport," Papers 2103.11435, arXiv.org, revised Dec 2022.

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