IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v47y2011i2p159-163.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000085
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, January.
    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.
    3. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    4. Igor V. Evstigneev & Klaus Schürger & Michael I. Taksar, 2004. "On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang‐Bang No‐Arbitrage Criteria," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 201-221, April.
    5. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    6. 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.
    7. (**), 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.
    8. 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.
    9. repec:dau:papers:123456789/5630 is not listed on IDEAS
    10. repec:crs:wpaper:9513 is not listed on IDEAS
    11. 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.
    12. Fulvio Ortu, 2001. "Arbitrage, linear programming and martingales¶in securities markets with bid-ask spreads," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(2), pages 79-105, November.
    13. repec:dau:papers:123456789/5647 is not listed on IDEAS
    14. 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.
    15. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    16. repec:crs:wpaper:9514 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Tomasz Zastawniak, 2024. "Fundamental Theorem of Asset Pricing under fixed and proportional costs in multi-asset setting and finite probability space," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 137-149, June.
    5. 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.
    6. 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.
    7. Esmaeil Babaei, 2024. "Asset pricing and hedging in financial markets with fixed and proportional transaction costs," Annals of Finance, Springer, vol. 20(2), pages 259-275, June.
    8. 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.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    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. Matteo Burzoni, 2015. "Arbitrage and Hedging in model-independent markets with frictions," Papers 1512.01488, arXiv.org, revised Aug 2016.
    4. 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.
    5. 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.
    6. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    7. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
    8. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    9. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    10. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics, Market Frictions, and Capital Growth," Economics Discussion Paper Series 1816, Economics, The University of Manchester.
    11. Paolo Guasoni & Emmanuel Lépinette & Miklós Rásonyi, 2012. "The fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 16(4), pages 741-777, October.
    12. Christoph Czichowsky & Johannes Muhle-Karbe & Walter Schachermayer, 2012. "Transaction Costs, Shadow Prices, and Duality in Discrete Time," Papers 1205.4643, arXiv.org, revised Jan 2014.
    13. Tomasz Zastawniak, 2024. "Fundamental Theorem of Asset Pricing under fixed and proportional costs in multi-asset setting and finite probability space," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 137-149, June.
    14. 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.
    15. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics and Capital Growth in Financial Markets with Frictions," Economics Discussion Paper Series 1815, Economics, The University of Manchester.
    16. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    17. Robert Jarrow & Philip Protter & Sergio Pulido, 2015. "The Effect Of Trading Futures On Short Sale Constraints," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 311-338, April.
    18. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    19. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    20. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:159-163. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.