A test of efficiency for the S&P 500 index option market using the generalized spectrum method

This paper examines the efficiency of the S&P 500 options market by testing the martingale properties of the Model-Free Forward Variance (MFFV) time series using the Generalized Spectral Test (GST). Based on a sample from January 1, 1996 to May 31, 2010, our tests show robust evidence that the S&P 500 options market is not efficient. By examining the subsamples before and after the 2008 financial crisis, we find this options market inefficiency is mainly driven by the outbreak of the subprime crisis. Our diagnostic tests further indicate that this inefficiency is due to the skewness-in-mean effect of forward variance. Specifically, the skewness-in-mean effect is weakened once we account for the S&P 500 index jump effects. Hence, we can establish a link between jumps and options market inefficiency. Finally, we find that the lagged skewness of the forward variance can help forecasting the forward variance both in-sample and out-of-sample. The economic significance of this forecasting ability is further highlighted by the performance of a trading strategy based on forward variance. In sum, out study provides robust evidence and a trading implication on testing the S&P 500 options market efficiency.