probability, while probabilities are derived from an estimated stochastic volatility model of the form GARCH components with …

of stochastic volatility and jumps for option valuation. This example highlights the impact on option 'smirks' of the … joint distribution of jumps in volatility and jumps in the underlying asset price, through both amplitude as well as jump …

The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility … more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the … CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and …

We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude …-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in … stochastic volatility. The model features correlations between innovations to futures prices and volatility, quasi …

We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index … about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex …

-dependent options and options on assets with stochastic volatility and jumps. " …

competing explanations: stochastic volatility models with negative correlations between market levels and volatilities, and … squares/Kalman filtration methodology. While volatility and level shocks are substantially negatively correlated, the … stochastic volatility model can explain the implicit negative skewness only under extreme parameters (e.g., high volatility of …