Volatility risk premium implications of GARCH option pricing models

- 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.

In this paper we explore important implications of capturing volatility risk premium (VRP) within a parametric GARCH setting. We study the transmission mechanism of shocks from returns to risk-neutral volatility by providing an examination of the news-impact curves and impulse-response functions of risk-neutral volatility, in order to better understand how option prices respond to return innovations. We report a value of − 3% for the magnitude of the average VRP and we recover the empirical densities under physical and risk-neutral measures. Allowing for VRP is crucial for adding flexibility to the shape of the two distributions. In our estimation procedure, we adopt a MLE approach that incorporates both physical return and risk-neutral VIX dynamics. By introducing volatility - instead of variance - innovations in the joint likelihood function and by allowing for contemporaneous correlation between innovations in returns and the VIX we show that we may critically reduce the bias and improve the efficiency of the joint maximum likelihood estimator, especially for the parameters of the volatility process. Modeling returns and the VIX as a bi-variate normal permits identification of a contemporaneous correlation coefficient of approximately − 30% between returns and risk-neutral volatility.