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A class of options with stochastic lives and an extension of the Black-Scholes formula |
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| Institution: | 1. Chair for Information Systems Research, University of Freiburg, 79098 Freiburg, Germany;2. National Institute of Informatics (NII), 2-1-2 Hitotsubashi, Tokyo 101-8430, Japan;1. Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012, USA;2. Zicklin School of Business, Baruch College, 55 Lexington Ave, New York, NY, 10010, USA |
| Abstract: | Certain options have a fixed date of maturity but may be cancelled prematurely. This can happen for a stock option in case of a merger or for an executive stock option in case the executive leaves his/her present job. The differential equation is given which governs the value of an option with a stochastic life. Solutions can be obtained through integration in certain cases. The main result is an extension of the Black-Scholes formula to options where the time to expiration is stochastic. |
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