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Weak transport for non‐convex costs and model‐independence in a fixed‐income market

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  • Beatrice Acciaio
  • Mathias Beiglböck
  • Gudmund Pammer

Abstract

We consider a model‐independent pricing problem in a fixed‐income market and show that it leads to a weak optimal transport problem as introduced by Gozlan et al. We use this to characterize the extremal models for the pricing of caplets on the spot rate and to establish a first robust super‐replication result that is applicable to fixed‐income markets. Notably, the weak transport problem exhibits a cost function which is non‐convex and thus not covered by the standard assumptions of the theory. In an independent section, we establish that weak transport problems for general costs can be reduced to equivalent problems that do satisfy the convexity assumption, extending the scope of weak transport theory. This part could be of its own interest independent of our financial application, and is accessible to readers who are not familiar with mathematical finance notation.

Suggested Citation

  • Beatrice Acciaio & Mathias Beiglböck & Gudmund Pammer, 2021. "Weak transport for non‐convex costs and model‐independence in a fixed‐income market," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1423-1453, October.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:4:p:1423-1453
    DOI: 10.1111/mafi.12328
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    References listed on IDEAS

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    1. Constantinos Daskalakis & Alan Deckelbaum & Christos Tzamos, 2017. "Strong Duality for a Multiple‐Good Monopolist," Econometrica, Econometric Society, vol. 85, pages 735-767, May.
    2. Mathias Beiglbock & Benjamin Jourdain & William Margheriti & Gudmund Pammer, 2021. "Stability of the Weak Martingale Optimal Transport Problem," Papers 2109.06322, arXiv.org, revised Apr 2022.
    3. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    4. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    5. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    6. Aurélien Alfonsi & Jacopo Corbetta & Benjamin Jourdain, 2019. "Sampling Of One-Dimensional Probability Measures In The Convex Order And Computation Of Robust Option Price Bounds," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-41, May.
    7. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    8. Aurélien Alfonsi & Jacopo Corbetta & Benjamin Jourdain, 2020. "Sampling of probability measures in the convex order by Wasserstein projection," Post-Print hal-01589581, HAL.
    9. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
    10. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    11. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
    12. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
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