The Implied Convexity of VIX Futures

The Journal of Derivatives, 2016

18 Pages Posted: 17 Apr 2019

See all articles by Robert T. Daigler

Robert T. Daigler

Florida International University (FIU) - Department of Finance

Brice V. Dupoyet

Florida International University - College of Business Administration - Finance

Fernando Patterson

North Carolina Central University (NCCU)

Date Written: March 20, 2016

Abstract

An important component of theoretical CBOE Volatility Index (VIX) futures prices is a term correcting for the negative convexity of the square root function by subtracting from the forward-starting variance swap rate an estimate of the future volatility of VIX futures prices. In the same fashion that an index option’s traditional implied volatility can be viewed as an aggregate market consensus of future realized volatility, this convexity value can be viewed as an aggregate market consensus of future volatility of volatility. This article examines the predictive properties and features of this convexity adjustment needed to value VIX futures prices by extracting it from the relationship between observed VIX futures prices and the corresponding spot option market prices used to compute the forward-starting variance swap rate. The authors find that implied convexity levels can indeed be used to forecast the future volatility of VIX futures prices, even though implied convexity consistently underestimates future realized VIX futures variance. They also show that implied convexity can at times violate strict theoretical conditions by being negative, although we are able to rule out arbitrage opportunities. Finally, they examine the properties of this implied convexity adjustment, both as a time series and with respect to various market volatility factors with which they find positive and statistically significant relations.

Keywords: Implied Convexity, VIX Futures Variance, Volatility

JEL Classification: G12; G13; G17

Suggested Citation

Daigler, Robert T. and Dupoyet, Brice and Patterson, Fernando, The Implied Convexity of VIX Futures (March 20, 2016). The Journal of Derivatives, 2016. Available at SSRN: https://ssrn.com/abstract=3356624

Robert T. Daigler

Florida International University (FIU) - Department of Finance ( email )

University Park
11200 SW 8th Street
Miami, FL 33199
United States
305-348-3325 (Phone)
305-348-4245 (Fax)

Brice Dupoyet (Contact Author)

Florida International University - College of Business Administration - Finance ( email )

University Park, RB 209 A
11200 SW 8th Street
Miami, FL 33199
United States
305-348-3328 (Phone)
305-348-4245 (Fax)

Fernando Patterson

North Carolina Central University (NCCU) ( email )

Durham, NC 27707
United States

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