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The Journal of Derivatives

The Journal of Derivatives

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Article

The Implied Convexity of VIX Futures

Robert T. Daigler, Brice Dupoyet and Fernando M. Patterson
The Journal of Derivatives Spring 2016, 23 (3) 73-90; DOI: https://doi.org/10.3905/jod.2016.23.3.073
Robert T. Daigler
is Knight Ridder Research Professor of Finance at Florida International University in Miami, FL. daiglerr@fiu.edu
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Brice Dupoyet
is an associate professor of finance at Florida International University in Miami, FL. dupoyetb@fiu.edu
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Fernando M. Patterson
is an assistant professor of finance at the University of Texas Rio Grande Valley in Edinburg, Texas. fernando.patterson@utrgv.edu
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Abstract

With the advent of modern option theory and practice, volatility has become one of the most important financial variables. The CBOE Volatility Index (VIX) of implied volatility for the S&P 500 Index has spawned numerous similar volatility indexes for other asset classes and a profusion of VIX-related futures, options, and exchange-traded funds (ETFs). But even though variance is nicely behaved, rising linearly in proportion to the length of the holding period, the square root of variance volatility is nonlinear. Variance is easy to hedge with a linear forward contract, but volatility is not. A convexity correction for the curvature of the square root function is needed. This correction is a function of the volatility of volatility (i.e., of the VIX in this case), which is an object of considerable interest in its own right. In this article, Daigler, Dupoyet, and Patterson make use of the convexity correction relationship to extract implied convexity from the difference between the price of a variance swap and the square of implied volatility from options on VIX futures. Although the relationship is a little noisy in the data, implied convexity, which is the “vol of VIX,” behaves largely as one expects. The authors’ insight may offer a new and useful estimator for this important parameter.

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The Journal of Derivatives: 23 (3)
The Journal of Derivatives
Vol. 23, Issue 3
Spring 2016
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The Implied Convexity of VIX Futures
Robert T. Daigler, Brice Dupoyet, Fernando M. Patterson
The Journal of Derivatives Feb 2016, 23 (3) 73-90; DOI: 10.3905/jod.2016.23.3.073

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The Implied Convexity of VIX Futures
Robert T. Daigler, Brice Dupoyet, Fernando M. Patterson
The Journal of Derivatives Feb 2016, 23 (3) 73-90; DOI: 10.3905/jod.2016.23.3.073
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  • Article
    • Abstract
    • A BRIEF LOOK AT CURRENT MODELS OF VIX FUTURES PRICING
    • METHODOLOGY
    • DATA
    • IMPLIED CONVEXITY PROPERTIES AND RESULTS
    • POTENTIAL VIOLATIONS OF THE MODEL
    • CONCLUSION
    • ENDNOTES
    • REFERENCES
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More in this TOC Section

  • An Alternative Option to Portfolio Rebalancing
  • Editor’s Letter
  • The Second Partial Derivative of Option Price with Respect to the Strike: A Historical Reminiscence
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