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Path integral approach to Asian options in the Black–Scholes model

Author

Listed:
  • Devreese, J.P.A.
  • Lemmens, D.
  • Tempere, J.

Abstract

We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:4:p:780-788
    DOI: 10.1016/j.physa.2009.10.020
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Capuozzo, Pietro & Panella, Emanuele & Schettini Gherardini, Tancredi & Vvedensky, Dimitri D., 2021. "Path integral Monte Carlo method for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    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. 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.
    5. Alexander Lipton, 2023. "Kelvin Waves, Klein-Kramers and Kolmogorov Equations, Path-Dependent Financial Instruments: Survey and New Results," Papers 2309.04547, arXiv.org.
    6. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    7. Leonardo Perotti & Lech A. Grzelak, 2022. "On Pricing of Discrete Asian and Lookback Options under the Heston Model," Papers 2211.03638, arXiv.org, revised Feb 2024.
    8. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    9. 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.
    10. Shafi, Khuram & Latif, Natasha & Shad, Shafqat Ali & Idrees, Zahra & Gulzar, Saqib, 2018. "Estimating option greeks under the stochastic volatility using simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1288-1296.
    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. 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.
    14. 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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