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Expected Optimal Exercise Time of a Perpetual American Option: A Closed-form Solution

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Abstract

Using martingale methods, we find that the expected optimal exercise time of a perpetual, dividend-paying American call option contract is: the ratio of the time-independent stopping boundary to the risk-adjusted drift of the stock price process. This ratio is an analytical expression. Of independent interest is the computational simplicity of our derivation. Specifically, we use only the optional sampling theorem of martingale theory and elementary algebra. In contrast, the non-martingale approach requires tedious integration and solution of an ordinary differential equation.

I am particularly indebted to Profs. I. Karatzas and M. Tamarkin for advice and encouragement as well as to E. Henning for technical comments. Finally, this research was partially supported by the Institute for Mathematics and its Applications—University of Minnesota, with funds provided by the U.S. National Science Foundation.

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Author information

Authors and Affiliations

  1. Graduate School of Management, Clark University, 950 Main Street, Worcester, Massachusetts, USA, 01610

    Rudy Yaksick (Lecturer, Research Associate)

  2. Dept. of Finance and Economics, Boston University, USA

    Rudy Yaksick (Lecturer, Research Associate)

  3. Center for the Study of Financial Engineering, USA

    Rudy Yaksick (Lecturer, Research Associate)

Authors
  1. Rudy Yaksick
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Editor information

Editors and Affiliations

  1. Centre for Data Analysis and Stochastic Processes, Free University Brussels, Brussels, Belgium

    Jacques Janssen

  2. Department of Production Engineering and Management, Technical University of Crete, Chania, Crete, Greece

    Christos H. Skiadas  & Constantin Zopounidis  & 

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© 1995 Springer Science+Business Media Dordrecht

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Yaksick, R. (1995). Expected Optimal Exercise Time of a Perpetual American Option: A Closed-form Solution. In: Janssen, J., Skiadas, C.H., Zopounidis, C. (eds) Advances in Stochastic Modelling and Data Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0663-6_2

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  • DOI: https://doi.org/10.1007/978-94-017-0663-6_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4574-4

  • Online ISBN: 978-94-017-0663-6

  • eBook Packages: Springer Book Archive

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