Perpetual Call Options with Non-Tradability

Optimal Control Applications and Methods, Vol. 26, No. 3, pp. 107-127, 2005

Cass Business School Research Paper

Posted: 12 Dec 2004

See all articles by Ashay Kadam

Ashay Kadam

IIM Udaipur

Peter Lakner

New York University (NYU) - Department of Information, Operations, and Management Sciences

Anand Srinivasan

National University of Singapore - Department of Finance

Abstract

We explicitly solve an optimal stopping problem related to the exercise of a perpetual American call option when the option holder cannot trade the underlying asset. We prove the verification theorem for the solution proposed. We derive the moment generating function of the optimal exercise time and also the elasticity of the option value with respect to stock price. The class of admissible utility functions that we solve for contains the CRRA family with some parametric restrictions. This theoretical framework provides the exact exercise boundary and the value of perpetual real options for a self interested manager whose incentives are not aligned with those of the shareholders. It can also serve as an approximation to the valuation of executive stock options.

Keywords: Non-Tradability, Incomplete Markets, Real Options, Executive Stock Options, Optimal Stopping

Suggested Citation

Kadam, Ashay and Lakner, Peter and Srinivasan, Anand, Perpetual Call Options with Non-Tradability. Optimal Control Applications and Methods, Vol. 26, No. 3, pp. 107-127, 2005, Cass Business School Research Paper, Available at SSRN: https://ssrn.com/abstract=631201

Ashay Kadam (Contact Author)

IIM Udaipur ( email )

Mohanlal Sukhadia University Campus
Udaipur, Rajasthan 313001
India

Peter Lakner

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States
212-998-0476 (Phone)

Anand Srinivasan

National University of Singapore - Department of Finance ( email )

Mochtar Riady Building
15 Kent Ridge Drive
Singapore, 119245
Singapore

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