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- W2610199929 abstract "Abstract We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed‐form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX‐implied volatilities, and their sensitivities, in the joint limit of short time‐to‐maturity and small log‐moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol‐of‐vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications." @default.
- W2610199929 created "2017-05-12" @default.
- W2610199929 creator A5001028268 @default.
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- W2610199929 date "2018-10-11" @default.
- W2610199929 modified "2023-10-17" @default.
- W2610199929 title "The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework" @default.
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- W2610199929 doi "https://doi.org/10.1111/mafi.12196" @default.
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