Option pricing with fuzzy measures under Knightian uncertainty

Conventionally We describe the risk with a unique probability measure. However, Ellsberg paradox indicates that the existing of Knightian uncertainty would have an effect on both decision-makers' behavior and asset pricing. In this paper we propose an option pricing model under Knightian uncertainty using the λ-fuzzy measure and the Choquet integral, and we get the equilibrium price of European option on a non-dividend-paying stock. The equilibrium price is an interval instead of a determinate number, which is in accordance with Epstein's conclusion. Subsequently we do an empirical research and the outcome indicate that parameter A which can describe human subjective sentimental will change with volatility of personal mood. Moreover, this will pave a new way to cope with other derivatives pricing under Knightian uncertainty.