We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More precisely, we discuss a discrete time dynamics in which...

We derive an analytic relation between equity risk premium and the term structure of variance risk premium (VRP). Motivated by this result, we estimate the VRP term structure using a general and fully analytical discrete-time option pricing framework featuring multiple volatility components and...

The new digital revolution of big data is deeply changing our capability of understanding society and forecasting the outcome of many social and economic systems. Unfortunately, information can be very heterogeneous in the importance, relevance, and surprise it conveys, affecting severely the...