Excess Movement in Option‐Implied Beliefs

ABSTRACT We derive bounds on the rational variation in option‐implied beliefs about market returns. While risk preferences distort option‐implied (or risk‐neutral ) beliefs away from subjective beliefs, one can nonetheless bound risk‐neutral belief movement under a general assumption on the stochastic discount factor. The resulting test requires no knowledge of the objective distribution and allows significantly more flexibility in discount rates than standard volatility tests. Implementing our test empirically using index options, we find that there is so much movement in risk‐neutral beliefs that the bounds are routinely violated. Our results imply significant excess index‐price volatility.