IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v02y1999i04ns0219024999000200.html
   My bibliography  Save this article

A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results

Author

Listed:
  • ELEONORA BENNATI

    (Dipartimento di Scienze, Economiche dell'Università di Pisa, Via Curtatone e Montanara, 14 56100 Pisa, Italy)

  • MARCO ROSA-CLOT

    (Dipartimento di Fisica, Università degli Studi di Firenze and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Largo Enrico Fermi 2, I-50125, Firenze, Italy)

  • STEFANO TADDEI

    (Dipartimento di Fisica, Università degli Studi di Firenze and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Largo Enrico Fermi 2, I-50125, Firenze, Italy)

Abstract

We use a path integral approach for solving the stochastic equations underlying the financial markets, and show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the multi-dimensional cases, with point dependent drift and volatility, and describe a covariant formulation which allows general changes of variables. Finally we apply the method to some economic models with analytical solutions. In particular, we evaluate the expectation value of functionals which correspond to quantities of financial interest.

Suggested Citation

  • Eleonora Bennati & Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 381-407.
    • Handle: RePEc:wsi:ijtafx:v:02:y:1999:i:04:n:s0219024999000200
    DOI: 10.1142/S0219024999000200
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024999000200
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024999000200?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.

    Citations

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


    Cited by:

    1. Andrew Matacz, 2000. "Path dependent option pricing: the path integral partial averaging method," Science & Finance (CFM) working paper archive 500034, Science & Finance, Capital Fund Management.
    2. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    3. Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
    4. Yu. A. Kuperin & P. A. Poloskov, 2010. "Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatility," Papers 1009.4587, arXiv.org.
    5. Paolinelli, Giovanni & Arioli, Gianni, 2018. "A path integral based model for stocks and order dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 387-399.
    6. Bustamante, M. & Contreras, M., 2016. "Multi-asset Black–Scholes model as a variable second class constrained dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 540-572.
    7. G., Mauricio Contreras & Peña, Juan Pablo, 2019. "The quantum dark side of the optimal control theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 450-473.
    8. Cassagnes, Aurelien & Chen, Yu & Ohashi, Hirotada, 2014. "Path integral pricing of outside barrier Asian options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 266-276.
    9. Moore, Ryleigh A. & Narayan, Akil, 2022. "Adaptive density tracking by quadrature for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    10. Yu. A. Kuperin & P. A. Poloskov, 2010. "American Options Pricing under Stochastic Volatility: Approximation of the Early Exercise Surface and Monte Carlo Simulations," Papers 1009.5495, arXiv.org.
    11. Paolinelli, Giovanni & Arioli, Gianni, 2019. "A model for stocks dynamics based on a non-Gaussian path integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 499-514.
    12. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    13. Marco Rosa-Clot & Stefano Taddei, 2002. "A Path Integral Approach To Derivative Security Pricing Ii: Numerical Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 123-146.
    14. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.
    15. Igor Halperin, 2021. "Distributional Offline Continuous-Time Reinforcement Learning with Neural Physics-Informed PDEs (SciPhy RL for DOCTR-L)," Papers 2104.01040, arXiv.org.

    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:wsi:ijtafx:v:02:y:1999:i:04:n:s0219024999000200. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.