In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...

We address potential strengths and weaknesses of alternative protection schemes, which can be adopted as a ‘default option' in a private, third pillar, pension product. In light of the observed behavior of savers adopting the ‘default option' at international level, we perform a comparative...

This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of...