ABSTRACT

We use model-independent statistical tools to demonstrate the presence of a short time-scale, on the order of days, in S&P500 volatility. The data are high-frequency and we discuss the inherent problems due to the “day effect”. We show that the presence of a well-separated longer time-scale does not affect our analysis. On the other hand, we explain why this short scale has to be dealt with in option pricing. We assess the sensitivity of this estimate using simulations from a stochastic volatility model calibrated roughly to the data.