Calculating the Index of Volatility in Inhomogeneous Levy Models

Abstract

The problem of calculating an analog of volatility index (VIX) in exponential Levy models is considered. To obtain the relation for the original index, an assumption is made about the market diffusion model. Unlike Levy models, diffusion models are not able to describe sharp changes of asset prices and offer a poorer calibration flexibility. Relations for calculating an analog of VIX for the exponential Levy model are therefore used, including one with a determinate time change. An explicit form of the relation for the index computation is obtained for the special case of the gamma dispersion model.