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...

The shape of the VIX term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. A single principal component, Slope, summarizes nearly all this information, predicting the excess returns of S&P 500...

This paper documents law of one price violations in equity volatility markets. While tightly linked by no-arbitrage restrictions, the prices of VIX futures exhibit significant deviations relative to their option-implied upper bounds. Static arbitrage opportunities occur when the prices of VIX...

This paper provides empirical evidence that volatility markets are integrated through the time-varying term structure of variance risk premia. These risk premia predict the returns from selling volatility for different horizons, maturities, and products, including variance swaps, straddles, and...