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...