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 develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates …

Given a European derivative security with an arbitrary payoff function and a corresponding set of" underlying … securities on which the derivative security is based, we solve the dynamic replication problem: find a" self-financing dynamic …-dependent options and options on assets with stochastic volatility and jumps. " …

We document a new stylized fact regarding the term-structure of futures volatility. We show that …consistent with the aforementioned "V-shape" relation between the volatility of futures prices and …in time-varying volatility of futures prices. Calibrating this model, we show it is quantitatively …

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 …

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic … volatility models, and implements it to analyze models of S&P 500 index volatility. Volatility models are compared by their … ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black …

An efficient method is developed for pricing American options on combination stochastic volatility …/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable, thereby nesting two major option pricing … models. The parameters implicit in PHLX-traded Deutschemark options of the stochastic volatility/jump- diffusion model and …

, including influential studies identifying price bubbles in periods of high volatility. Here we consider a model of the market …