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Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions

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  • Kleinert, Hagen

Abstract

Within a path integral formalism for non-Gaussian price fluctuations, we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is evaluated for truncated Lèvy distributions.

Suggested Citation

  • Kleinert, Hagen, 2002. "Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 217-242.
    • Handle: RePEc:eee:phsmap:v:312:y:2002:i:1:p:217-242
    DOI: 10.1016/S0378-4371(02)00839-7
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    Citations

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    Cited by:

    1. 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.
    2. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    3. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
    4. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    5. Kakushadze, Zura, 2017. "Volatility smile as relativistic effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 59-76.
    6. 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.
    7. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    8. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    9. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    10. 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.
    11. 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.
    12. DECAMPS, Marc & DE SCHEPPER, Ann & GOOVAERTS, Marc, "undated". "Path integrals as a tool for pricing interest rate contingent claims: The case of reflecting and absorbing boundaries," Working Papers 2003027, University of Antwerp, Faculty of Business and Economics.

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