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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 Beiglboeck
  • 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 notations.

Suggested Citation

  • Beatrice Acciaio & Mathias Beiglboeck & Gudmund Pammer, 2020. "Weak Transport for Non-Convex Costs and Model-independence in a Fixed-Income Market," Papers 2011.04274, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2011.04274
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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. Luciano Campi & Ismail Laachir & Claude Martini, 2017. "Change of numeraire in the two-marginals martingale transport problem," Finance and Stochastics, Springer, vol. 21(2), pages 471-486, April.
    3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    4. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    5. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    6. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    7. 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.
    8. 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.
    9. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    10. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    11. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
    12. Aurélien Alfonsi & Jacopo Corbetta & Benjamin Jourdain, 2020. "Sampling of probability measures in the convex order by Wasserstein projection," Post-Print hal-01589581, HAL.
    13. 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.
    14. Julio Backhoff-Veraguas & Gudmund Pammer, 2019. "Stability of martingale optimal transport and weak optimal transport," Papers 1904.04171, arXiv.org, revised Dec 2020.
    15. 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.
    16. Campi, Luciano & Laachir, Ismail & Martini, Claude, 2017. "Change of numeraire in the two-marginals martingale transport problem," LSE Research Online Documents on Economics 68783, London School of Economics and Political Science, LSE Library.
    17. 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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