Call options with concave payoffs: An application to executive stock options

Abstract

We observe that the incentive effects of traditional stock options can be improved by making the option's payoff concave in the region of a high stock price at maturity. To reflect the concave property, we propose two types of executive stock options: a generalized power option and an ordinary bull spread. Under the [Hall and Murphy (): American Economic Review 209‐214, Hall and Murphy () Journal of Accounting and Economics 33: 3‐42] framework, we show that the generalized power option with high concavity and the ordinary bull spread generate greater incentive effects than those of traditional options or the [Bernard, Boyle, and Chen (): The Journal of Derivatives 23: 9‐20] power executive options.