IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v38y2018i8p958-976.html
   My bibliography  Save this article

Modeling VXX

Author

Listed:
  • Sebastian A. Gehricke
  • Jin E. Zhang

Abstract

In this paper, we study the VXX Exchange Traded Note (ETN), that has been actively traded in recent years, but has lost 99.84% of its value. Using Zhang's formula for VIX futures prices, we develop the first theoretical model for the VXX that links the SPX, VIX, and VXX. We show that the roll yield of VIX futures drives the difference between the VXX and VIX returns. The roll yield is a mostly negative process. We then provide a simple yet robust estimation of the market price of variance risk using VXX and VIX futures prices. The model can be used to price VXX options.

Suggested Citation

  • Sebastian A. Gehricke & Jin E. Zhang, 2018. "Modeling VXX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(8), pages 958-976, August.
  • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:8:p:958-976
    DOI: 10.1002/fut.21913
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.21913
    Download Restriction: no

    File URL: https://libkey.io/10.1002/fut.21913?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    4. 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.
    5. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
    6. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    7. Jinghong Shu & Jin E. Zhang, 2012. "Causality in the VIX futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(1), pages 24-46, January.
    8. Duan, Jin-Chuan & Yeh, Chung-Ying, 2010. "Jump and volatility risk premiums implied by VIX," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2232-2244, November.
    9. Nicolas P.B. Bollen & Michael J. O'Neill & Robert E. Whaley, 2017. "Tail Wags Dog: Intraday Price Discovery in VIX Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(5), pages 431-451, May.
    10. Carol Alexander & Dimitris Korovilas, 2012. "Diversification of Equity with VIX Futures: Personal Views and Skewness Preference," ICMA Centre Discussion Papers in Finance icma-dp2012-07, Henley Business School, University of Reading.
    11. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    12. 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.
    13. Bao, Qunfang & Li, Shenghong & Gong, Donggeng, 2012. "Pricing VXX option with default risk and positive volatility skew," European Journal of Operational Research, Elsevier, vol. 223(1), pages 246-255.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    16. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.
    17. 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.
    18. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    19. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sebastian A. Gehricke & Jin E. Zhang, 2020. "Modeling VXX under jump diffusion with stochastic long‐term mean," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(10), pages 1508-1534, October.
    2. Gonzalez-Perez, Maria T., 2015. "Model-free volatility indexes in the financial literature: A review," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 141-159.
    3. Xingguo Luo & Jin E. Zhang & Wenjun Zhang, 2019. "Instantaneous squared VIX and VIX derivatives," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1193-1213, October.
    4. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Robert Azencott & Yutheeka Gadhyan & Roland Glowinski, 2014. "Option Pricing Accuracy for Estimated Heston Models," Papers 1404.4014, arXiv.org, revised Jul 2015.
    7. Zhe Zhao & Zhenyu Cui & Ionuţ Florescu, 2018. "VIX derivatives valuation and estimation based on closed-form series expansions," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-18, June.
    8. Eraker, Bjørn & Wang, Jiakou, 2015. "A non-linear dynamic model of the variance risk premium," Journal of Econometrics, Elsevier, vol. 187(2), pages 547-556.
    9. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    10. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    11. R. Merino & J. Pospíšil & T. Sobotka & J. Vives, 2018. "Decomposition Formula For Jump Diffusion Models," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-36, December.
    12. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Josep Vives, 2019. "Decomposition formula for jump diffusion models," Papers 1906.06930, arXiv.org.
    13. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    14. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
    15. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, December.
    16. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, July-Dece.
    17. Daniel Guterding, 2020. "Inventory effects on the price dynamics of VSTOXX futures quantified via machine learning," Papers 2002.08207, arXiv.org.
    18. Naoto Kunitomo & Yong‐Jin Kim, 2007. "Effects Of Stochastic Interest Rates And Volatility On Contingent Claims," The Japanese Economic Review, Japanese Economic Association, vol. 58(1), pages 71-106, March.
    19. Changfu Ma & Wei Xu & Yue Kuen Kwok, 2020. "Willow tree algorithms for pricing VIX derivatives under stochastic volatility models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-28, March.
    20. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2011.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jfutmk:v:38:y:2018:i:8:p:958-976. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0270-7314/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.