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The path integral representation kernel of evolution operator in Merton-Garman model

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  • L. F. Blazhyevskyi
  • V. S. Yanishevsky

Abstract

In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.

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  • L. F. Blazhyevskyi & V. S. Yanishevsky, 2011. "The path integral representation kernel of evolution operator in Merton-Garman model," Papers 1106.5143, arXiv.org.
    • Handle: RePEc:arx:papers:1106.5143
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    File URL: http://arxiv.org/pdf/1106.5143
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    Cited by:

    1. Xavier Calmet & Nathaniel Wiesendanger Shaw, 2020. "An analytical perturbative solution to the Merton–Garman model using symmetries," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(1), pages 3-22, January.
    2. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    3. Xavier Calmet & Nathaniel Wiesendanger Shaw, 2019. "An analytical perturbative solution to the Merton Garman model using symmetries," Papers 1909.01413, arXiv.org, revised Jan 2021.
    4. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.

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