This paper proposes a robust semiparametric bootstrap method to estimate predictive distributions of GARCH-type models. The method is based on a robust estimation of parametric GARCH models and a robustified resampling scheme for GARCH residuals that controls bootstrap instability due to...

Realized divergence gauges the distinct realized moments associated with time-varying uncertainty and is tradeable with divergence swaps engineered from delta-hedged option portfolios. Consistently with established notions of symmetry in arbitrage-free option markets, implied divergence...

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...