We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes … inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that … the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility …

The volatility premium is a well-documented phenomenon, which can be approximated by the difference between the … previous month level of the VIX Index and the rolling 30-day close-to-close volatility. In concordance with existing literature …, we show evidence that VIX is generally above the 30-day rolling volatility giving rise to the volatility premium, so that …

implemented and do not contain any numerical integration.These formulas are important in volatility surface construction and CMS …

Stochastic volatility models are widely used in interest rate modeling to match the option smiles -- the two most …, Heston-LMM and SABR-LMM respectively.In this paper we consider the CEV model with a general stochastic volatility. Assuming … that rate-volatility correlation is zero we are able to obtain an exact integral representation of the option price …

Conventional financial theory considers ex-ante that risk, generally measured by the volatility, has to be …

which depending on the market states signaled by the level of volatility spread. We have documented that effectively, there … capital. We then propose the volatility spread as the active management factor into the Carhart's model used to evaluate …