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The Fine Structure of Variance: Pricing VIX Derivatives in Consistent and Log-VIX Models

63 Pages Posted: 25 Mar 2012 Last revised: 18 Aug 2016

Nicole Branger

University of Muenster - Finance Center Muenster

Alexander Kraftschik

University of Muenster - Finance Center Muenster

Clemens Völkert

University of Muenster - Finance Center Muenster

Date Written: August 17, 2016

Abstract

We analyze pricing models for VIX derivatives which account for the theoretical link to stock options, taking Log-VIX models as a benchmark. We focus on up to three risk factors to model variance risk. To assess the performance of the models, we do not only look at the pricing errors, but also at the level and dynamics of the VIX' risk-neutral moments which vary considerably over time. We find that both model classes, consistent- and Log-VIX models, can reproduce the empirical patterns if three risk factors are included. In both approaches, a stochastic central tendency is of first order importance to capture the term structure of VIX futures prices, i.e. the first moment of the risk-neutral distribution. A stochastic vol-of-vol then helps to match the prices of VIX options, i.e. the higher order moments. Finally, variance jumps add the finishing touches to the model performance. All in all, consistency comes at notable costs in-sample, while out-of-sample performances are close. We find that the main difference between both model classes is the ability to capture the second moment of the VIX risk-neutral distribution.

Keywords: Consistent pricing of VIX derivatives, Log-VIX model, volatility derivatives, VIX

JEL Classification: G13

Suggested Citation

Branger, Nicole and Kraftschik, Alexander and Völkert, Clemens, The Fine Structure of Variance: Pricing VIX Derivatives in Consistent and Log-VIX Models (August 17, 2016). Available at SSRN: https://ssrn.com/abstract=2028285 or http://dx.doi.org/10.2139/ssrn.2028285

Nicole Branger

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=162

Alexander Kraftschik

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=3737

Clemens Völkert (Contact Author)

University of Muenster - Finance Center Muenster ( email )

Universitätsstr. 14-16
Münster, 48143
Germany

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