I use option prices to infer real-time moments of stochastic discount factors (SDFs). The moments are estimated, from daily SP 500 index option data, in real time, without relying on past observations. These moments are forward-looking and significantly predict the market excess return. The...

In this paper, we develop lower bounds on the variance of the permanent component and the transitory component, and on the variance of the ratio of the permanent to the transitory components of SDFs. Exactly solved eigenfunction problems are then used to study the empirical attributes of asset...