to approximate the conditional volatility, quantified with a GARCH(1,1) process, that is observed in empirical price data … investigate the two most prominent puzzles related to low-frequency stock prices: The conditional volatility of price returns, and …

volatility across di.erent time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that … a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time … horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state …

Based on the APARCH model and two outlier detection methods, we computereliable time series of volatility asymmetry for … mostcountries. We nd that economic development and market capitalization/GDP arethe most important factors that increase volatility …

We show that the volatility of a price process, which is usuallyregarded as an impediment to financial growth, can serve …

and Stein stochastic volatility model driven by two correlated Brownian motion. It turns out that in case the mean …

various assumptions about the underlying price process including large drifts, stochastic volatility with leverage effects and … futures data sampled at a 5-minute frequency. A state-space framework reveals the latent stochastic volatility process and …