Options Can Induce Risk Taking for Arbitrary Preferences

Abstract

It is widely believed that call options induce risk-taking behavior. However, Ross (2003) challenges this intuition by demonstrating the impossibility of inducing managers with arbitrary preferences to always act as if less risk averse. If preferences and price distributions are unknown, risk-taking behavior cannot be induced by options. Here, we prove a new result showing that, with absolutely no information about preferences and some knowledge about prices, one can write a call option that makes all managers prefer riskier projects to safer ones. This points out that in order to design options that induce risk taking it is sufficient to have information about price distributions.

Keywords: Stochastic Dominance, Stock Options, Risk Taking

JEL Classification: D81, G00, J33, M21