IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1808.03607.html
   My bibliography  Save this paper

"Quantum Equilibrium-Disequilibrium": Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons

Author

Listed:
  • Igor Halperin
  • Matthew Dixon

Abstract

We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism. Using a linear market impact model, this produces a non-linear two-parametric extension of the classical Geometric Brownian Motion (GBM) model, that we call the "Quantum Equilibrium-Disequilibrium" (QED) model. The QED model gives rise to non-linear mean-reverting dynamics, broken scale invariance, and corporate defaults. In the simplest one-stock (1D) formulation, our parsimonious model has only one degree of freedom, yet calibrates to both equity returns and credit default swap spreads. Defaults and market crashes are associated with dissipative tunneling events, and correspond to instanton (saddle-point) solutions of the model. When market frictions and inflows/outflows of money are neglected altogether, "classical" GBM scale-invariant dynamics with an exponential asset growth and without defaults are formally recovered from the QED dynamics. However, we argue that this is only a formal mathematical limit, and in reality the GBM limit is non-analytic due to non-linear effects that produce both defaults and divergence of perturbation theory in a small market friction parameter.

Suggested Citation

  • Igor Halperin & Matthew Dixon, 2018. ""Quantum Equilibrium-Disequilibrium": Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons," Papers 1808.03607, arXiv.org, revised May 2019.
  • Handle: RePEc:arx:papers:1808.03607
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1808.03607
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    2. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. Jan W Dash, 2004. "Quantitative Finance and Risk Management:A Physicist's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5436, February.
    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. Mirosław Lachowicz & Henryk Leszczyński, 2020. "Modeling Asymmetric Interactions in Economy," Mathematics, MDPI, vol. 8(4), pages 1-14, April.

    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. Halperin, Igor & Dixon, Matthew, 2020. "“Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    3. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    4. Hong-Ming Yin & Jin Liang & Yuan Wu, 2018. "On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate," JRFM, MDPI, vol. 11(4), pages 1-12, December.
    5. Navarrete, Eduardo, 2012. "Modeling optimal pine stands harvest under stochastic wood stock and price in Chile," Forest Policy and Economics, Elsevier, vol. 15(C), pages 54-59.
    6. Kaido Kepp & Kadri Männasoo, 2021. "Investment irreversibility and cyclical adversity: Implications for the financial performance of European manufacturing companies," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(7), pages 1665-1678, October.
    7. Adrian Lei & Martin Yick & Keith Lam, 2013. "Does tax convexity matter for risk? A dynamic study of tax asymmetry and equity beta," Review of Quantitative Finance and Accounting, Springer, vol. 41(1), pages 131-147, July.
    8. Decamps, Jean-Paul & Faure-Grimaud, Antoine, 2002. "Excessive continuation and dynamic agency costs of debt," European Economic Review, Elsevier, vol. 46(9), pages 1623-1644, October.
    9. Hui Chen & Jianjun Miao & Neng Wang, 2010. "Entrepreneurial Finance and Nondiversifiable Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(12), pages 4348-4388, December.
    10. Rose Neng Lai & Lawrence Hoc Nang Fong, 2021. "Development Strategies in a Market of High Vacancies and Sticky Rates – The Case of the Hotel Industry," International Real Estate Review, Global Social Science Institute, vol. 24(3), pages 363-383.
    11. Lu, Jin-Ray & Hwang, Chih-Chiang & Lin, Chien-Yi, 2016. "Do shareholders appreciate capital investment policies of corporations?," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 344-353.
    12. Kyung Shim & Harjoat Bhamra, 2015. "Stochastic Idiosyncratic Operating Risk and Real Options: Implications for Stock Returns," 2015 Meeting Papers 1494, Society for Economic Dynamics.
    13. Anderson, Ronald W. & Sundaresan, Suresh & Tychon, Pierre, 1996. "Strategic analysis of contingent claims," European Economic Review, Elsevier, vol. 40(3-5), pages 871-881, April.
    14. Flor, Christian Riis & Petersen, Kirstine Boye & Schandlbauer, Alexander, 2023. "Callable or convertible debt? The role of debt overhang and covenants," Journal of Corporate Finance, Elsevier, vol. 78(C).
    15. Shibata, Takashi & Nishihara, Michi, 2015. "Investment-based financing constraints and debt renegotiation," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 79-92.
    16. Delong Li & Mr. Nicolas E Magud & Mr. Fabian Valencia, 2015. "Corporate Investment in Emerging Markets: Financing vs. Real Options Channel," IMF Working Papers 2015/285, International Monetary Fund.
    17. Aabo, Tom & Pantzalis, Christos & Park, Jung Chul & Trigeorgis, Lenos & Wulff, Jesper N., 2024. "CEO personality traits, strategic flexibility, and firm dynamics," Journal of Corporate Finance, Elsevier, vol. 84(C).
    18. Adriana Breccia & William Perraudin, 2010. "Debt Valuation and Chapter 22," Birkbeck Working Papers in Economics and Finance 1015, Birkbeck, Department of Economics, Mathematics & Statistics.
    19. Luis Alvarez, 2010. "Irreversible capital accumulation under interest rate uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 249-271, October.
    20. Pryshchepa, Oksana & Aretz, Kevin & Banerjee, Shantanu, 2013. "Can investors restrict managerial behavior in distressed firms?," Journal of Corporate Finance, Elsevier, vol. 23(C), pages 222-239.

    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:1808.03607. 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.