The lead-lag relation between spot and option markets and implied volatility in option prices

We show that if a lead-lag relation exists between the option and spot markets, the implied volatility in option prices can be biased depending on the level of the true volatility; that is, the higher the true volatility, the more upward biased the implied volatility will be. We then test the theoretical conjecture, using intraday transactions data of the S&P 500 stock index and its options. The empirical results show that the S&P 500 index option market leads the cash index, and that the bias of the implied volatility due to the lead-lag relation is statistically significant, confirming our theoretical conjecture.