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Model-free Representation of Pricing Rules as Conditional Expectations

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Sara BIAGINI

    (Università degli Studi di Perugia, Italy)

  • Rama CONT

    (Centre de Mathématiques Appliquées, Ecole Polytechnique, France)

Abstract

We formulate an operational definition for absence of model-free arbitrage in a financial market, in terms of a set of minimal requirements for the pricing rule prevailing in the market and without making reference to any ‘objective’ probability measure. We show that any pricing rule verifying these properties can be represented as a conditional expectation operator with respect to a probability measure under which prices of traded assets follow martingales. Our result does not require any notion of “reference” probability measure and is consistent with the formulation of model calibration problems in option pricing.

Suggested Citation

  • Sara BIAGINI & Rama CONT, 2007. "Model-free Representation of Pricing Rules as Conditional Expectations," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 3, pages 53-66, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0003
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    Citations

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    Cited by:

    1. Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, vol. 15(3), pages 573-605, September.
    2. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    3. Christian Bender & Sebastian E. Ferrando & Alfredo L. Gonzalez, 2021. "Conditional Non-Lattice Integration, Pricing and Superhedging," Papers 2105.12072, arXiv.org.
    4. Christian Bender & Sebastian Ferrando & Alfredo Gonzalez, 2021. "Model-Free Finance and Non-Lattice Integration," Papers 2105.10623, arXiv.org.

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