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Path dependent option pricing: the path integral partial averaging method

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  • Andrew Matacz

    (Science & Finance, Capital Fund Management)

Abstract

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one dimensional integral. I illustrate the application of the method to Asian options and occupation time derivatives.

Suggested Citation

  • 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.
    • Handle: RePEc:sfi:sfiwpa:500034
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    References listed on IDEAS

    as
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    5. 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.
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    8. Carl Chiarella & Nadima El-Hassan & Adam Kucera, 2004. "Evaluation of Point Barrier Options in a Path Integral Framework Using Fourier-Hermite Expansions," Research Paper Series 126, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. 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.
    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. 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.
    4. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.

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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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