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American options on assets with dividends near expiry

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

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..

Suggested Citation

  • J. D. Evans & R. Kuske & Joseph B. Keller, 2002. "American options on assets with dividends near expiry," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 219-237.
  • Handle: RePEc:bla:mathfi:v:12:y:2002:i:3:p:219-237
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    References listed on IDEAS

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    Cited by:

    1. Maria do Rosário Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function," Working Papers REM 2017/19, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    2. Maria do Rosário Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Pricing American Call Option by the Black-Scholes Equation with a Nonlinear Volatility Function," Working Papers REM 2017/18, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    3. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, pages 157-192.
    4. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2015. "Real Options and American Derivatives: The Double Continuation Region," Management Science, INFORMS, pages 1094-1107.
    5. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    6. Maria do Rosario Grossinho & Yaser Kord Faghan & Daniel Sevcovic, 2016. "Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function," Papers 1611.00885, arXiv.org, revised Nov 2017.
    7. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, pages 75-99.
    8. 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.
    9. Maria do Rosario Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Pricing American Call Options by the Black-Scholes Equation with a Nonlinear Volatility Function," Papers 1707.00358, arXiv.org.
    10. 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.
    11. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2015. "Real Options and American Derivatives: The Double Continuation Region," Management Science, INFORMS, pages 1094-1107.
    12. 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.
    13. 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.
    14. repec:kap:apfinm:v:24:y:2017:i:4:d:10.1007_s10690-017-9234-1 is not listed on IDEAS

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