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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

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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    1. repec:dau:papers:123456789/5630 is not listed on IDEAS
    2. Shunming Zhang & Chunlei Xu & Xiaotie Deng, 2002. "Dynamic Arbitrage-Free Asset Pricing with Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 89-97.
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    7. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    8. (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
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    10. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    11. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
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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. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    3. 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.
    4. 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.
    5. repec:wsi:ijtafx:v:20:y:2017:i:02:n:s021902491750011x is not listed on IDEAS

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