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American options on assets with dividends near expiry

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  • J. D. Evans
  • R. Kuske
  • Joseph B. Keller
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    Abstract

    Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate "D" to the interest rate "r". For "D">"r" the put boundary near expiry tends parabolically to the value "rK"/"D" where "K" is the strike price, while for "D" "r" the boundary tends to "K" in the parabolic-logarithmic form found for the case "D"=0 by Barles et al. (1995) and by Kuske and Keller (1998). For the call, these two behaviors are interchanged: parabolic and tending to "rK"/"D" for "D">"r", as was shown by Wilmott, Dewynne, and Howison (1993), and parabolic-logarithmic and tending to "K" for "D" "r". The results are derived twice: once by solving an integral equation, and again by constructing matched asymptotic expansions. Copyright 2002 Blackwell Publishing, Inc..

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 12 (2002)
    Issue (Month): 3 ()
    Pages: 219-237

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    Handle: RePEc:bla:mathfi:v:12:y:2002:i:3:p:219-237

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    Cited by:
    1. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    2. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
    3. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
    4. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    5. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    6. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2013. "Real Options and American Derivatives: the Double Continuation Region," Working Papers 499, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Zhu, Song-Ping & Chen, Wen-Ting, 2013. "An inverse finite element method for pricing American options," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 231-250.

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