The cross-sectional relation between conditional heteroskedasticity, the implied volatility smile, and the variance risk premium

•Implied volatility smiles and variance risk premia are compared across different markets.•The implied volatility smile is related to time-series conditional heteroskedasticity.•The variance risk premium is related to time-series conditional heteroskedasticity.•Determinants of the implied volatility smile and variance risk premium are identified.

This paper estimates how the shape of the implied volatility smile and the size of the variance risk premium relate to parameters of GARCH-type time-series models measuring how conditional volatility responds to return shocks. Markets in which return shocks lead to large increases in conditional volatility tend to have larger variance risk premia than markets in which the impact on conditional volatility is slight. Markets in which negative (positive) return shocks lead to larger increases in future volatility than positive (negative) return shocks tend to have downward (upward) sloping implied volatility smiles. Also, differences in how volatility responds to return shocks as measured by GARCH-type models explain much, but not all, of the variations in excess kurtosis and multi-period skewness across different markets.