By means of classical Itô’s calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due by correlation and a term due to the volatility of the volatility. This decomposition allows us to develop …rst and second-order approximation formulas for option prices and implied vol...

Forecasting volatility has received a great deal of research attention. Many articles have considered the relative performance of econometric model based and option implied volatility forecasts. While many studies have found that implied volatility is the preferred approach, a number of issues remain unresolved. One issue being the relative merit of combination forecasts. By utilising recent ec...

We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread conjecture is given. keywords: local vol, Dupire’s formula; MSC: 91G99; JEL: G10.

The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score. Keywords: Duration models; g...

German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after calibrating for the Merton jump diffusion (MJD), variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman, Madan and Yor (CGMY) and the Black and Scholes (B&S) model. Implied volatility is examined...

We develop a multivariate generalization of the Markov–switching GARCH model introduced by Haas, Mittnik, and Paolella (2004b) and derive its fourth– moment structure. An application to international stock markets illustrates the relevance of accounting for volatility regimes from both a statistical and economic perspective, including out–of–sample portfolio selection and computation of Value– ...

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in the information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variabl...