Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.

This paper provides a method for testing for regime differences when regimes are long-lasting. Standard testing procedures are generally inappropriate because regime persistence causes a spurious regression problem – a problem that has led to incorrect inference in a broad range of studies involving regimes representing political, business, and seasonal cycles. The paper outlines analytically how standard estimators can be adjusted for regime dummy variable persistence. While the adjustments are helpful asymptotically, spurious regression remains a problem in small samples and must be addressed using simulation or bootstrap procedures. We provide a simulation procedure for testing hypotheses in situations where an independent variable in a time-series regression is a persistent regime dummy variable. We also develop a procedure for testing hypotheses in situations where the dependent variable has similar properties.