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

Rudy Yaksick ()
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Rudy Yaksick: Clark University, Graduate School of Management

A chapter in Advances in Stochastic Modelling and Data Analysis, 1995, pp 29-56 from Springer

Abstract: 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.

Keywords: Brownian motion; First passage time; Martingale; American call option; Optimal exercise (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0663-6_2

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DOI: 10.1007/978-94-017-0663-6_2

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