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Pricing without no-arbitrage condition in discrete time

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  • Laurence Carassus
  • Emmanuel L'epinette

Abstract

In a discrete time setting, we study the central problem of giving a fair price to some financial product. For several decades, the no-arbitrage conditions and the martingale measures have played a major role for solving this problem. We propose a new approach for estimating the super-replication cost based on convex duality instead of martingale measures duality: The prices are expressed using Fenchel conjugate and bi-conjugate without using any no-arbitrage condition.The super-hedging problem resolution leads endogenously to a weak no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which prices are finite. We study this condition in details, propose several characterizations and compare it to the no-arbitrage condition.

Suggested Citation

  • Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.
    • Handle: RePEc:arx:papers:2104.02688
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    References listed on IDEAS

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    Cited by:

    1. Dorsaf Cherif & Emmanuel Lépinette, 2023. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Post-Print hal-03284660, HAL.
    2. Sergey Smirnov & Dimitri Sotnikov & Andrey Zanochkin, 2024. "Approximation and asymptotics in the superhedging problem for binary options," Annals of Finance, Springer, vol. 20(4), pages 421-458, December.
    3. Meriam El Mansour & Emmanuel Lepinette, 2023. "Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty," Papers 2311.08847, arXiv.org.
    4. repec:hal:wpaper:hal-03284660 is not listed on IDEAS

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