Temporal Price Relation Between Stock and Option Markets and a Bias of Implied Volatility in Option Prices

We show that if a particular temporal 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. The higher the true volatility, the more upward (downward) biased the implied volatility will be, if the option market leads (lags) the spot market. Using intraday data of the S&P 500 index options, we show that the option market leads the spot market at least in the sample. More importantly, the implied volatility is biased due to the lead-lag relationship, and the bias is more profound when the market is more volatile.