IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i3d10.1007_s11009-023-10049-8.html
   My bibliography  Save this article

A Non-equilibrium Geometric No-arbitrage Principle

Author

Listed:
  • Wanxiao Tang

    (Nanjing University of Science and Technology)

  • Peibiao Zhao

    (Nanjing University of Science and Technology)

Abstract

The present paper gets a novel and intimate correspondence between martingale in finances and one-parameter transform group in mathematics. This article confirms a criteria of the no-arbitrage problem in a frictionless financial market and a frictional financial market under the conformal transformation via this correspondence. The geometric no-arbitrage principle posed here also reveals a pricing principle on manifolds.

Suggested Citation

  • Wanxiao Tang & Peibiao Zhao, 2023. "A Non-equilibrium Geometric No-arbitrage Principle," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-15, September.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10049-8
    DOI: 10.1007/s11009-023-10049-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10049-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-023-10049-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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. 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.
    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. 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.
    2. Georgy Chabakauri & Kathy Yuan & Konstantinos E Zachariadis, 2022. "Multi-asset Noisy Rational Expectations Equilibrium with Contingent Claims [A Noisy Rational Expectations Equilibrium for Multi-asset Securities Markets]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2445-2490.
    3. Fischer, Stanley & Merton, Robert C., 1984. "Macroeconomics and finance: The role of the stock market," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 21(1), pages 57-108, January.
    4. 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.
    5. Jian Guo & Saizhuo Wang & Lionel M. Ni & Heung-Yeung Shum, 2022. "Quant 4.0: Engineering Quantitative Investment with Automated, Explainable and Knowledge-driven Artificial Intelligence," Papers 2301.04020, arXiv.org.
    6. 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.
    7. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    8. David Daewhan Cho, 2004. "Uncertainty in Second Moments: Implications for Portfolio Allocation," Econometric Society 2004 Far Eastern Meetings 433, Econometric Society.
    9. William R. Emmons & Frank A. Schmid, 2000. "The Asian crisis and the exposure of large U.S. firms," Review, Federal Reserve Bank of St. Louis, vol. 82(Jan), pages 15-34.
    10. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Stafylas, Dimitrios & Anderson, Keith & Uddin, Moshfique, 2017. "Recent advances in explaining hedge fund returns: Implicit factors and exposures," Global Finance Journal, Elsevier, vol. 33(C), pages 69-87.
    12. Climent Hernández José Antonio & Venegas Martínez Francisco, 2013. "Valuación de opciones sobre subyacentes con rendimientos a-estables," Contaduría y Administración, Accounting and Management, vol. 58(4), pages 119-150, octubre-d.
    13. Jack S. K. Chang & Jean C. H. Loo & Carolyn C. Wu Chang, 1990. "The Pricing Of Futures Contracts And The Arbitrage Pricing Theory," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 297-306, December.
    14. Ferreira, Eva & Gil-Bazo, Javier & Orbe, Susan, 2008. "Nonparametric estimation of conditional beta pricing models," DEE - Working Papers. Business Economics. WB wb082403, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    15. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2013.
    16. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    17. Chen, Shiyi & Chng, Michael T. & Liu, Qingfu, 2021. "The implied arbitrage mechanism in financial markets," Journal of Econometrics, Elsevier, vol. 222(1), pages 468-483.
    18. Ion STANCU & Laura OBREJABRAŞOVEANU & Anamaria CIOBANU & Andrei Tudor STANCU, 2017. "Are Company Valuation Models the Same? – A Comparative Analysis between the Discounted Cash Flows (DCF), the Adjusted Net Asset, Value and Price Multiples, the Market Value Added (MVA) and the Residua," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(3), pages 5-20.
    19. Markus Bibinger & Per A. Mykland, 2013. "Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing," SFB 649 Discussion Papers SFB649DP2013-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    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:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10049-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.