State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion

It has been widely noted in the empirical literature that state-price densities implicit in financial asset prices are not log-normal. This paper shows that this phenomenon can be caused by heterogeneity in investors’ beliefs. It derives the state-price density under heterogeneous beliefs in closed form and demonstrates that heterogeneous beliefs can give rise to multimodal state-price densities. Consequences for the “smile effect” in implied option volatility and for measures of risk aversion inferred from empirical state-price densities are discussed.