We explore important implications of volatility risk premium (VRP) within a parametric GARCH setting.

Study the transmission mechanism of shocks from returns to risk-neutral volatility through NICs and IRFs.

Adopt a Joint-MLE to incorporate both physical return and risk-neutral VIX dynamics and uncover a contemporaneous correlation of -30% between them.

Reduce the bias and improve the efficiency of the J-MLE for the parameters of the volatility process.

Report a value of −3% for the average VRP and jointly recover the empirical densities under the two measures.