IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1709.07446.html
   My bibliography  Save this paper

Arbitrage and Geometry

Author

Listed:
  • Daniel Q. Naiman
  • Edward R. Scheinerman

Abstract

This article introduces the notion of arbitrage for a situation involving a collection of investments and a payoff matrix describing the return to an investor of each investment under each of a set of possible scenarios. We explain the Arbitrage Theorem, discuss its geometric meaning, and show its equivalence to Farkas' Lemma. We then ask a seemingly innocent question: given a random payoff matrix, what is the probability of an arbitrage opportunity? This question leads to some interesting geometry involving hyperplane arrangements and related topics.

Suggested Citation

  • Daniel Q. Naiman & Edward R. Scheinerman, 2017. "Arbitrage and Geometry," Papers 1709.07446, arXiv.org.
    • Handle: RePEc:arx:papers:1709.07446
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1709.07446
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Varian, Hal R, 1987. "The Arbitrage Principle in Financial Economics," Journal of Economic Perspectives, American Economic Association, vol. 1(2), pages 55-72, Fall.
    Full references (including those not matched with items on IDEAS)

    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. repec:dau:papers:123456789/5374 is not listed on IDEAS
    2. Keith A. Lewis, 2019. "A Simple Proof of the Fundamental Theorem of Asset Pricing," Papers 1912.01091, arXiv.org.
    3. Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    4. Wanxiao Tang & Jun Zhao & Peibiao Zhao, 2019. "Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs," JRFM, MDPI, vol. 12(1), pages 1-17, February.
    5. Perrakis, Stylianos, 1989. "Les contributions de la théorie financière à la solution de problèmes en organisation industrielle et en microéconomie appliquée," L'Actualité Economique, Société Canadienne de Science Economique, vol. 65(4), pages 518-546, décembre.
    6. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    7. Kallio, Markku & Ziemba, William T., 2007. "Using Tucker's theorem of the alternative to simplify, review and expand discrete arbitrage theory," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2281-2302, August.
    8. Saggese, Pietro & Belmonte, Alessandro & Dimitri, Nicola & Facchini, Angelo & Böhme, Rainer, 2023. "Arbitrageurs in the Bitcoin ecosystem: Evidence from user-level trading patterns in the Mt. Gox exchange platform," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 251-270.
    9. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    10. Carmen López-Martín & Sonia Benito Muela & Raquel Arguedas, 2021. "Efficiency in cryptocurrency markets: new evidence," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(3), pages 403-431, September.
    11. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    12. Sebastián A. Rey, 2016. "The Valuation of Equities and the GDP Growth Effect: A Global Empirical Study," IJFS, MDPI, vol. 4(4), pages 1-18, October.
    13. Dan W. French & Edwin D. Maberly, 1992. "Early Exercise Of American Index Options," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 15(2), pages 127-137, June.
    14. Nietert, Bernhard & Wilhelm, Jochen, 2001. "Some economic remarks on arbitrage theory," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 7, University of Passau, Faculty of Business and Economics.
    15. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    16. Hunter, William C. & Smith, Stephen D., 2002. "Risk management in the global economy: A review essay," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 205-221, March.
    17. Jos'e Manuel Corcuera, 2021. "The Golden Age of the Mathematical Finance," Papers 2102.06693, arXiv.org, revised Mar 2021.
    18. Iivo Vehvilainen, 2002. "Basics of electricity derivative pricing in competitive markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 45-60.
    19. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Peter Carr & Dilip Madan, 2012. "Factor Models for Option Pricing," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(4), pages 319-329, November.
    21. Joseph K. Cheung & John Heaney, 1990. "A contingent†claim integration of cost†volume†profit analysis with capital budgeting," Contemporary Accounting Research, John Wiley & Sons, vol. 6(2), pages 738-760, March.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1709.07446. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.