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A dimension‐invariant cascade model for VIX futures

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  • Zhiguang Wang
  • Brice Dupoyet

Abstract

We propose a new stochastic volatility model by allowing for a cascading structure of volatility components. The model, under a minor assumption, allows us to add as many components as desired with no additional parameters, effectively defeating the curse of dimensionality often encountered in traditional models. We derive a semi‐closed‐form solution to the VIX futures price, and find that our six‐factor model with only six parameters can closely fit spot VIX and VIX futures prices from 2004 to 2015 and produce out‐of‐sample pricing errors of magnitudes similar to those of in‐sample errors.

Suggested Citation

  • Zhiguang Wang & Brice Dupoyet, 2019. "A dimension‐invariant cascade model for VIX futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1214-1227, October.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:10:p:1214-1227
    DOI: 10.1002/fut.22042
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    References listed on IDEAS

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    1. Yingzi Zhu & Jin E. Zhang, 2007. "Variance Term Structure And Vix Futures Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 111-127.
    2. Peter Carr & Liuren Wu, 2010. "Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 8(4), pages 409-449, Fall.
    3. Jin E. Zhang & Yuqin Huang, 2010. "The CBOE S&P 500 three‐month variance futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(1), pages 48-70, January.
    4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    5. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    6. Yueh‐Neng Lin, 2007. "Pricing VIX futures: Evidence from integrated physical and risk‐neutral probability measures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(12), pages 1175-1217, December.
    7. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    8. Xingguo Luo & Jin E. Zhang, 2012. "The Term Structure of VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(12), pages 1092-1123, December.
    9. Jin E. Zhang & Jinghong Shu & Menachem Brenner, 2010. "The new market for volatility trading," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(9), pages 809-833, September.
    10. Egloff, Daniel & Leippold, Markus & Wu, Liuren, 2010. "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1279-1310, October.
    11. Zhongjin Lu & Yingzi Zhu, 2010. "Volatility components: The term structure dynamics of VIX futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(3), pages 230-256, March.
    12. Calvet, Laurent E. & Fisher, Adlai J. & Wu, Liuren, 2018. "Staying on Top of the Curve: A Cascade Model of Term Structure Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(2), pages 937-963, April.
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