IDEAS home Printed from https://ideas.repec.org/p/arx/papers/cond-mat-0407321.html
   My bibliography  Save this paper

Pricing Exotic Options in a Path Integral Approach

Author

Listed:
  • G. Bormetti
  • G. Montagna
  • N. Moreni
  • O. Nicrosini

Abstract

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances.

Suggested Citation

  • G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2004. "Pricing Exotic Options in a Path Integral Approach," Papers cond-mat/0407321, arXiv.org, revised May 2006.
    • Handle: RePEc:arx:papers:cond-mat/0407321
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/cond-mat/0407321
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
    3. Marco Airoldi, 2004. "A perturbative moment approach to option pricing," Papers cond-mat/0401503, arXiv.org.
    4. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
    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. 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.
    2. 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.
    3. Cassagnes, Aurelien & Chen, Yu & Ohashi, Hirotada, 2014. "Path integral pricing of Wasabi option in the Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 1-10.
    4. Devreese, J.P.A. & Lemmens, D. & Tempere, J., 2010. "Path integral approach to Asian options in the Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 780-788.
    5. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    6. Giacomo Bormetti & Sofia Cazzaniga, 2011. "Multiplicative noise, fast convolution, and pricing," Papers 1107.1451, arXiv.org.
    7. Anantya Bhatnagar & Dimitri D. Vvedensky, 2022. "Quantum effects in an expanded Black–Scholes model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-12, August.
    8. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    9. Ma, Chao & Ma, Qinghua & Yao, Haixiang & Hou, Tiancheng, 2018. "An accurate European option pricing model under Fractional Stable Process based on Feynman Path Integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 87-117.
    10. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    11. Giacomo Bormetti & Giorgia Callegaro & Giulia Livieri & Andrea Pallavicini, 2015. "A backward Monte Carlo approach to exotic option pricing," Papers 1511.00848, arXiv.org.
    12. Giacomo Bormetti & Sofia Cazzaniga, 2014. "Multiplicative noise, fast convolution and pricing," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 481-494, March.
    13. 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.
    14. Axel A. Araneda & Marcelo J. Villena, 2018. "Computing the CEV option pricing formula using the semiclassical approximation of path integral," Papers 1803.10376, arXiv.org.
    15. Khaliq, A.Q.M. & Voss, D.A. & Yousuf, M., 2007. "Pricing exotic options with L-stable Pade schemes," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3438-3461, November.

    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. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2006. "Pricing exotic options in a path integral approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 55-66.
    2. Luca Capriotti, 2006. "The Exponent Expansion: An Effective Approximation Of Transition Probabilities Of Diffusion Processes And Pricing Kernels Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1179-1199.
    3. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    4. Fabrizio Pomponio & Frédéric Abergel, 2013. "Multiple-limit trades : empirical facts and application to lead-lag measures," Post-Print hal-00745317, HAL.
    5. Lubashevsky, Ihor & Friedrich, Rudolf & Heuer, Andreas & Ushakov, Andrey, 2009. "Generalized superstatistics of nonequilibrium Markovian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4535-4550.
    6. 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.
    7. Sebastiano Michele Zema & Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2021. "Mesoscopic Structure of the Stock Market and Portfolio Optimization," Papers 2112.06544, arXiv.org.
    8. S. Reimann, 2007. "Price dynamics from a simple multiplicative random process model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(4), pages 381-394, April.
    9. Dror Y. Kenett & Xuqing Huang & Irena Vodenska & Shlomo Havlin & H. Eugene Stanley, 2015. "Partial correlation analysis: applications for financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 15(4), pages 569-578, April.
    10. W.-S. Jung & F. Z. Wang & S. Havlin & T. Kaizoji & H.-T. Moon & H. E. Stanley, 2008. "Volatility return intervals analysis of the Japanese market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(1), pages 113-119, March.
    11. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    12. Xiao, Di & Wang, Jun, 2021. "Attitude interaction for financial price behaviours by contact system with small-world network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    13. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    14. V. Alfi & L. Pietronero & A. Zaccaria, 2008. "Minimal Agent Based Model For The Origin And Self-Organization Of Stylized Facts In Financial Markets," Papers 0807.1888, arXiv.org.
    15. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    16. Slanina, František, 2010. "A contribution to the systematics of stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3230-3239.
    17. Dibeh, Ghassan, 2007. "Contagion effects in a chartist–fundamentalist model with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 52-57.
    18. Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2013. "Option pricing with discrete time jump processes," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2417-2445.
    19. Till Massing, 2018. "Simulation of Student–Lévy processes using series representations," Computational Statistics, Springer, vol. 33(4), pages 1649-1685, December.
    20. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.

    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:cond-mat/0407321. 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.