We give an overview of a broad class of models designed to capture stochastic volatility in financial markets, with illustrations of the scope of application of these models to practical finance problems. In a broad sense, this model class includes GARCH, but we focus on a narrower set of...

The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility index, can be hard to measure with accuracy due to the lack of precise prices for options with strikes in the tails of the return distribution. This is reflected in practice as the...

This paper investigates long-run dependencies of volatility and volume, supposing that are driven by the same informative process. Log-realized volatility and log-volume are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component....