IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i8p2636-2640.html
   My bibliography  Save this article

Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian

Author

Listed:
  • Jana, T.K.
  • Roy, P.

Abstract

We show that the non-Hermitian Black–Scholes Hamiltonian and its various generalizations are η-pseudo Hermitian. The metric operator η is explicitly constructed for this class of Hamiltonians. It is also shown that the effective Black–Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

Suggested Citation

  • Jana, T.K. & Roy, P., 2012. "Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2636-2640.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:8:p:2636-2640
    DOI: 10.1016/j.physa.2011.12.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111009095
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2011.12.012?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. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    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. Will Hicks, 2020. "Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing," Papers 2009.00360, arXiv.org, revised Apr 2021.
    2. Will Hicks, 2021. "Wild Randomness, and the application of Hyperbolic Diffusion in Financial Modelling," Papers 2101.04604, arXiv.org, revised Apr 2021.

    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. Zhang, Chao & Huang, Lu, 2010. "A quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5769-5775.
    2. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    3. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    4. Di Xiao & Jun Wang & Hongli Niu, 2016. "Volatility Analysis of Financial Agent-Based Market Dynamics from Stochastic Contact System," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 607-625, December.
    5. Jana, T.K. & Roy, P., 2011. "Supersymmetry in option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2350-2355.
    6. Liu, Haijun & Wang, Longfei, 2018. "The price momentum of stock in distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2336-2344.
    7. Jaehyung Choi, 2011. "Spontaneous symmetry breaking of arbitrage," Papers 1107.5122, arXiv.org, revised Apr 2012.
    8. Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.
    9. Pedram, Pouria, 2012. "The minimal length uncertainty and the quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2100-2105.
    10. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the optimal allocation of assets in investment portfolio with application of modern portfolio and nonlinear dynamic chaos theories in investment, commercial and central banks," Papers 1301.4881, arXiv.org, revised Feb 2013.
    11. Bordley, Robert F., 2005. "Econophysics and individual choice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 479-495.
    12. Hongli Niu & Jun Wang, 2014. "Phase and multifractality analyses of random price time series by finite-range interacting biased voter system," Computational Statistics, Springer, vol. 29(5), pages 1045-1063, October.
    13. B. Zhang & J. Wang & W. Zhang & G. C. Wang, 2020. "Nonlinear Scaling Behavior of Visible Volatility Duration for Financial Statistical Physics Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 373-389, August.
    14. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    15. Cotfas, Liviu-Adrian, 2013. "A finite-dimensional quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 371-380.
    16. Zhang, Bo & Wang, Guochao & Wang, Yiduan & Zhang, Wei & Wang, Jun, 2019. "Multiscale statistical behaviors for Ising financial dynamics with continuum percolation jump," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1012-1025.
    17. Sabrina Camargo & Silvio M. Duarte Queiros & Celia Anteneodo, 2013. "Bridging stylized facts in finance and data non-stationarities," Papers 1302.3197, arXiv.org, revised May 2013.
    18. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    19. Laleh Tafakori & Armin Pourkhanali & Riccardo Rastelli, 2022. "Measuring systemic risk and contagion in the European financial network," Empirical Economics, Springer, vol. 63(1), pages 345-389, July.
    20. Alves, L.G.A. & Ribeiro, H.V. & Lenzi, E.K. & Mendes, R.S., 2014. "Empirical analysis on the connection between power-law distributions and allometries for urban indicators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 175-182.

    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:phsmap:v:391:y:2012:i:8:p:2636-2640. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.