Optimal exercise of executive stock options and implications for firm cost

This paper conducts a comprehensive study of the optimal exercise policy for an executive stock option and its implications for option cost, average life, and alternative valuation concepts. The paper is the first to provide analytical results for an executive with general concave utility. Wealthier or less risk-averse executives exercise later and create greater option cost. However, option cost can decline with volatility. We show when there exists a single exercise boundary, yet demonstrate the possibility of a split continuation region. We also show that, for constant relative risk averse utility, the option value does not converge to the Black and Scholes value as the correlation between the stock and the market portfolio converges to one. We compare our model’s option cost with the modified Black and Scholes approximation typically used in practice and show that the approximation error can be large or small, positive or negative, depending on firm characteristics. & 2010 Elsevier B.V. All rights reserved. All rights reserved. l Estate and Urban ul comments and arr, Darrell Duffie, , Yuanto Kusnadi, rt Mayhew, Kevin participants at the versity, Hong Kong val, Massachusetts ional University of Oxford University, niversity, Temple nd the 2007 China onference on the Markets, the 2008 the 2009 American teful to the referee ik Sen for valuable penter).