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Pricing exotic options in a path integral approach

Author

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

Abstract

In the framework of the 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, 2006. "Pricing exotic options in a path integral approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 55-66.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:1:p:55-66
    DOI: 10.1080/14697680500510878
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
    4. Marco Airoldi, 2004. "A perturbative moment approach to option pricing," Papers cond-mat/0401503, arXiv.org.
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    Citations

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    Cited by:

    1. Giacomo Bormetti & Sofia Cazzaniga, 2011. "Multiplicative noise, fast convolution, and pricing," Papers 1107.1451, arXiv.org.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Giacomo Bormetti & Sofia Cazzaniga, 2014. "Multiplicative noise, fast convolution and pricing," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 481-494, March.
    8. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    9. Giacomo Bormetti & Giorgia Callegaro & Giulia Livieri & Andrea Pallavicini, 2015. "A backward Monte Carlo approach to exotic option pricing," Papers 1511.00848, arXiv.org.
    10. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    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. 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.
    13. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    14. 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.
    15. 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.

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