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The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads

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  • Roux, Alet

Abstract

We establish the fundamental theorem of asset pricing to a model with proportional transaction costs on trading in shares and different interest rates for borrowing and lending of cash. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself free of arbitrage, i.e. if there exists an artificial friction-free price for the stock between its bid and ask prices and an artificial interest rate between the borrowing and lending interest rates such that, if one discounts this stock price by this interest rate, then the resulting process is a martingale under some equivalent probability measure.

Suggested Citation

  • Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:159-163
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    References listed on IDEAS

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    Cited by:

    1. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    2. Martin Brown & Tomasz Zastawniak, 2019. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Papers 1905.01859, arXiv.org, revised May 2019.
    3. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    4. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.
    5. Takuji Arai, 2016. "Good deal bounds with convex constraints: --- examples and proofs ---," Keio-IES Discussion Paper Series 2016-017, Institute for Economics Studies, Keio University.
    6. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    7. Takuji Arai, 2017. "Good Deal Bounds With Convex Constraints," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-15, March.

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