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A Term Structure Model for VIX Futures


  • The authors would like to thank two anonymous referees and Bob Webb (editor). Bujar Huskaj would also like to thank Hossein Asgharian, Hans Byström, Karl Larsson, Frederik Lundtofte, Kristian R. Miltersen, Birger Nilsson, Magnus Wiktorsson, and Anders Wilhelmsson.

Correspondence author, Department of Economics, Lund University, P.O. Box 7082, S-220 07 Lund, Sweden. Tel: +46 (0)46 222 95 49, Fax: +46 (0)46 222 41 18, e-mail:


This study develops a term structure model for VIX futures. Instead of deriving the VIX futures price from a model for the instantaneous variance of the S&P 500 or a model for the VIX, the VIX futures price dynamics are specified exogenously. The empirical features of VIX futures returns (positive skewness, excess kurtosis, and a decreasing volatility term structure for longer term expirations) are captured by assuming that they are normal inverse Gaussian distributed and scaled by a volatility function that is dependent on the maturity. The usefulness of the resulting model is illustrated in two applications: risk management (via calculating value at risk (VaR)) and asset pricing (via pricing hypothetical VIX options). The results show that the model provides a good fit for the empirical term structure of VIX futures, produces good VaR estimates, and is promising for use in pricing VIX options. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:421-442, 2013

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