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Perpetual American Defaultable Options in Models with Random Dividends and Partial Information

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  • Pavel V. Gapeev

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

  • Hessah Al Motairi

    (Department of Mathematics, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait)

Abstract

We present closed-form solutions to the perpetual American dividend-paying put and call option pricing problems in two extensions of the Black–Merton–Scholes model with random dividends under full and partial information. We assume that the dividend rate of the underlying asset price changes its value at a certain random time which has an exponential distribution and is independent of the standard Brownian motion driving the price of the underlying risky asset. In the full information version of the model, it is assumed that this time is observable to the option holder, while in the partial information version of the model, it is assumed that this time is unobservable to the option holder. The optimal exercise times are shown to be the first times at which the underlying risky asset price process hits certain constant levels. The proof is based on the solutions of the associated free-boundary problems and the applications of the change-of-variable formula.

Suggested Citation

  • Pavel V. Gapeev & Hessah Al Motairi, 2018. "Perpetual American Defaultable Options in Models with Random Dividends and Partial Information," Risks, MDPI, vol. 6(4), pages 1-15, November.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:127-:d:180978
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    References listed on IDEAS

    as
    1. Giuseppe Di Graziano & L. C. G. Rogers, 2009. "Equity with Markov-modulated dividends," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 19-26.
    2. Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.
    3. Zhengjun Jiang & Martijn Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Finance and Stochastics, Springer, vol. 12(3), pages 331-355, July.
    4. Erhan Bayraktar & Savas Dayanik, 2006. "Poisson Disorder Problem with Exponential Penalty for Delay," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 217-233, May.
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    Cited by:

    1. Zbigniew Palmowski & Paweł Stȩpniak, 2023. "Last-Passage American Cancelable Option in Lévy Models," JRFM, MDPI, vol. 16(2), pages 1-14, January.
    2. Gapeev, Pavel V. & Li, Libo, 2022. "Perpetual American standard and lookback options with event risk and asymmetric information," LSE Research Online Documents on Economics 114940, London School of Economics and Political Science, LSE Library.

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