A digitalized employee option

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.

Keywords:

• Employee option
• Exercise strategy
• Option valuation
• Optimal stopping
• Smooth fit at a single point

2000 Mathematics Subject Classification::

• 60G40
• 91B28

Acknowledgements

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

Notes

^¶ [email protected]

Additional information

Notes on contributors

B. Jensen

¶ ¶ [email protected]