Do Investors Need Kink to Cope with Ambiguity?

This study proposes a possible explanation for demand for derivatives that have kinks, such as plain vanilla options, using a market equilibrium model. In our setting, there is one risky asset and one ambiguous additive background risk, and a complete market exists for the risky asset. Under this environment, the optimal payoff function for an ambiguity-averse investor who has an exponential utility function exhibits kinks.