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.

中文翻译：

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非均匀征税模型中波动率的指数计算

考虑了在指数Levy模型中计算波动率指数（VIX）的模拟问题。为了获得原始指数的关系，对市场扩散模型进行了假设。与Levy模型不同，扩散模型无法描述资产价格的急剧变化，并且校准灵活性较差。因此，使用了用于计算指数Levy模型的VIX模拟量的关系，包括具有确定时间变化的关系。对于伽马色散模型的特殊情况，获得了用于索引计算的关系的显式形式。