Department of Economics and Business Economics

The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework

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DOI

  • Andrea Barletta
  • ,
  • Elisa Nicolato
  • Stefano Pagliarani, Università di Udine, Italy

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.

Original languageEnglish
JournalMathematical Finance
Volume29
Issue3
Pages (from-to)928-966
Number of pages39
ISSN0960-1627
DOIs
Publication statusPublished - 2019

    Research areas

  • C60, G12, G13, VIX options, asymptotic expansions, implied volatility asymptotics, multifactor stochastic volatility, CALIBRATION, EXPANSIONS, MODEL, OPTIONS, HESTON, TERM STRUCTURE, DYNAMICS, VARIANCE, SMILE, DEVIATIONS

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