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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 79, 2007 - Issue 1-2: Optimal Stopping and Applications Part I
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A digitalized employee option

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Pages 103-115 | Received 02 May 2006, Accepted 25 Oct 2006, Published online: 05 Nov 2008
 

Abstract

This paper introduces a new employee option plan for low- and mid-level employees. The option plan is a possibility for the employee to exercise an accrual account at any time before maturity contingent on the stock price being above a strike level. The option is American in nature and is a combination of an accrual account and a digital option with a strike price. The optimal stopping problem associated with the valuation of the option has a discontinuous payoff. The key argument to solve the stopping problem is the principle of smooth fit at a single point. The optimal exercise strategy is displayed and the valuation formula is derived.

2000 Mathematics Subject Classification::

Acknowledgements

The second author was supported by a Steno grant from the Danish Natural Science Research Council

Notes

Additional information

Notes on contributors

B. Jensen

¶ ¶ [email protected]

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