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Pricing Of Perpetual American Options In A Model With Partial Information

In: Finance at Fields

Author

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  • PAVEL V. GAPEEV

    (Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom)

Abstract

We study the perpetual American call option pricing problem in a model of a financial market in which the firm issuing a traded asset can regulate the dividend rate by switching it between two constant values. The firm dividend policy is unknown for small investors, who can only observe the prices available from the market. The asset price dynamics are described by a geometric Brownian motion with a random drift rate modeled by a continuous time Markov chain with two states. The optimal exercise time of the option for small investors is found as the first time at which the asset price hits a boundary depending on the current state of the filtering dividend rate estimate. The proof is based on an embedding of the initial problem into a two-dimensional optimal stopping problem and the analysis of the associated parabolic-type free-boundary problem. We also provide closed form estimates for the rational option price and the optimal exercise boundary.

Suggested Citation

  • Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 14, pages 327-347, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814407892_0014
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    Citations

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    Cited by:

    1. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    2. Gapeev, Pavel V., 2022. "Discounted optimal stopping problems in continuous hidden Markov models," LSE Research Online Documents on Economics 110493, London School of Economics and Political Science, LSE Library.
    3. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    4. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    5. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.
    6. Erik Ekström & Martin Vannestål, 2019. "American Options And Incomplete Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-14, September.
    7. Juozas Vaicenavicius, 2017. "Asset liquidation under drift uncertainty and regime-switching volatility," Papers 1701.08579, arXiv.org, revised Jan 2019.
    8. Erik Ekstrom & Juozas Vaicenavicius, 2015. "Optimal liquidation of an asset under drift uncertainty," Papers 1509.00686, arXiv.org.

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