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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
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000085
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    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 2 (March)
    Pages: 159-163

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:159-163
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

    Keywords: Fundamental theorem of asset pricing Proportional transaction costs Different borrowing and lending rates;

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    1. 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.
    2. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
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    4. 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.
    5. (**), 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.
    6. 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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    9. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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    11. 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.
    12. repec:crs:wpaper:9514 is not 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. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    3. Gianluca Cassese, 2014. "Asset Pricing in an Imperfect World," Papers 1410.6408, arXiv.org.
    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.

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