Before revision: We study the empirical properties of realized volatility of the E-mini S P 500 futures contract at various time scales, ranging from a few minutes to one day. Our main finding is that intraday volatility is remarkably rough and persistent. What is more, by further studying daily realized volatility measures of close to two thousand individual US equities, we find that both roughness and persistence appear to be universal properties of volatility. Inspired by the empirical findings, we introduce a new class of continuous-time stochastic volatility models, capable of decoupling roughness (short-term behavior) from long memoryand persistence (long-term behavior) in a simple and parsimonious way, which allows us to successfully model volatility at all intraday time scales .
After revision: We study the empirical properties of realized volatility of the E-mini S introduce a new class of continuous-time stochastic volatility models, capable of decoupling roughness (short-term behavior) from long memoryand persistence (long-term behavior) in a simple and parsimonious way, which allows us to successfully model volatility at all intraday time scales .