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Analytical Valuation of American Options on Jump‐Diffusion Processes

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  • Chandrasekhar Reddy Gukhal

Abstract

We derive analytic formulas for the value of American options when the underlying asset follows a jump‐diffusion process and pays continuous dividends. They early exercise premium has a form very different form from that for diffusion processes, and this can be attributed to the discontinuous nature of the price paths. Analytical formulas are derived for several distributions of the jump amplitude.

Suggested Citation

  • Chandrasekhar Reddy Gukhal, 2001. "Analytical Valuation of American Options on Jump‐Diffusion Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 97-115, January.
    • Handle: RePEc:bla:mathfi:v:11:y:2001:i:1:p:97-115
    DOI: 10.1111/1467-9965.00109
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    Cited by:

    1. Zhou, Qing & Zhang, Xili, 2020. "Pricing equity warrants in Merton jump–diffusion model with credit risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
    3. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2020. "A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics," Papers 2002.10194, arXiv.org.
    4. Gerald H. L. Cheang & Len Patrick Dominic M. Garces, 2020. "Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamics," Papers 2002.10202, arXiv.org.
    5. Gerald H. L. Cheang & Carl Chiarella & Andrew Ziogas, 2013. "The representation of American options prices under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 241-253, January.
    6. Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
    7. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, February.
    8. Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    9. Min Dai & Yue Kuen Kwok, 2006. "Characterization Of Optimal Stopping Regions Of American Asian And Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 63-82, January.
    10. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    11. Gerald Cheang & Carl Chiarella & Andrew Ziogas, 2009. "An Analysis of American Options Under Heston Stochastic Volatility and Jump-Diffusion Dynamics," Research Paper Series 256, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    13. Song-Ping Zhu & Guiyuan Ma, 2018. "An analytical solution for the HJB equation arising from the Merton problem," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-26, March.
    14. Li Chen & Guang Zhang, 2021. "Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processes," Papers 2104.11870, arXiv.org.
    15. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    16. Mr. Andre O Santos & Mr. Jorge A Chan-Lau, 2006. "Currency Mismatches and Corporate Default Risk: Modeling, Measurement, and Surveillance Applications," IMF Working Papers 2006/269, International Monetary Fund.
    17. Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2016. "American-style options in jump-diffusion models: estimation and evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1313-1324, August.

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