An analytical formula for VIX futures and its applications

Authors

  • Song-Ping Zhu,

    Corresponding author
    1. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia
    • School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, N.S.W. 2522, Australia
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  • Guang-Hua Lian

    1. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia
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  • The authors gratefully acknowledge the proofreading of the entire manuscript by, as well as many valuable comments from, Prof. Robert J. Elliott of the University of Adelaide, Australia.

Abstract

In this study we present a closed-form, exact solution for the pricing of VIX futures in a stochastic volatility model with simultaneous jumps in both the asset price and volatility processes. The newly derived formula is then used to show that the well-known convexity correction approximations can sometimes lead to large errors. Utilizing the newly derived formula, we also conduct an empirical study, the results of which demonstrate that the Heston stochastic volatility model is a good candidate for the pricing of VIX futures. While incorporating jumps into the underlying price can further improve the pricing of VIX futures, adding jumps to the volatility process appears to contribute little improvement for pricing VIX futures. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

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