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

In: Advances in Stochastic Modelling and Data Analysis

Author

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  • Rudy Yaksick

    (Clark University, Graduate School of Management
    Boston University, Dept. of Finance and Economics
    Center for the Study of Financial Engineering)

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.

Suggested Citation

  • Rudy Yaksick, 1995. "Expected Optimal Exercise Time of a Perpetual American Option: A Closed-form Solution," Springer Books, in: Jacques Janssen & Christos H. Skiadas & Constantin Zopounidis (ed.), Advances in Stochastic Modelling and Data Analysis, pages 29-56, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0663-6_2
    DOI: 10.1007/978-94-017-0663-6_2
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