The Expected Return and Exercise Time of Merton‐style Real Options

Mark Shackleton and Rafal Wojakowski

Journal of Business Finance & Accounting, 2002, vol. 29, issue 3‐4, 541-555

Abstract: We analyse the rate of return and expected exercise time of Merton‐style options (1973) employed in many real option situations where the possibility of exercise is both perpetual and American in nature. Using risk‐neutral and risk‐adjusted pricing techniques, Merton‐style options are shown to have an expected return that is a constant percentage of the option value and independent of the proximity to the critical exercise boundary. Merton options thus remain at the same point on the Security Market Line, unlike European options whose position and rate of return change dynamically. We also present formulae for the expected time and discounted times to exercise and analyse the dependency of these variables on volatility.

Date: 2002
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