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Convexity Of The Exercise Boundary Of The American Put Option On A Zero Dividend Asset

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  • Xinfu Chen
  • John Chadam
  • Lishang Jiang
  • Weian Zheng

Abstract

We show that the optimal exercise boundary for the American put option with non‐dividend‐paying asset is convex. With this convexity result, we then give a simple rigorous argument providing an accurate asymptotic behavior for the exercise boundary near expiry.

Suggested Citation

  • Xinfu Chen & John Chadam & Lishang Jiang & Weian Zheng, 2008. "Convexity Of The Exercise Boundary Of The American Put Option On A Zero Dividend Asset," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 185-197, January.
    • Handle: RePEc:bla:mathfi:v:18:y:2008:i:1:p:185-197
    DOI: 10.1111/j.1467-9965.2007.00328.x
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    References listed on IDEAS

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    Cited by:

    1. Wenting Chen & Kai Du & Xinzi Qiu, 2017. "Analytic properties of American option prices under a modified Black-Scholes equation with spatial fractional derivatives," Papers 1701.01515, arXiv.org.
    2. Raquel M. Gaspar & Sara D. Lopes & Bernardo Sequeira, 2020. "Neural Network Pricing of American Put Options," Risks, MDPI, vol. 8(3), pages 1-24, July.
    3. Daniel Sevcovic, 2008. "Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear Black-Scholes equations," Papers 0805.0611, arXiv.org.
    4. Jonas Al-Hadad & Zbigniew Palmowski, 2020. "Perpetual American options with asset-dependent discounting," Papers 2007.09419, arXiv.org, revised Jan 2021.
    5. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    6. Dejun Xie, 2009. "A Steady State Solution to a Mortgage Pricing Problem," Papers 0909.5389, arXiv.org.
    7. Jing Zhao & Hoi Ying Wong, 2012. "A closed-form solution to American options under general diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 725-737, July.
    8. Panagiota Daskalopoulos & Paul M. N. Feehan, 2011. "Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance," Papers 1109.1075, arXiv.org.

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