IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1506.07554.html
   My bibliography  Save this paper

Double-jump stochastic volatility model for VIX: evidence from VVIX

Author

Listed:
  • Xin Zang
  • Jun Ni
  • Jing-Zhi Huang
  • Lan Wu

Abstract

The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the existence of co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. With VVIX index as a proxy for the stochastic volatility, we use MCMC method to estimate the dynamics of VIX. Comparing nested models on VIX, we show the jump in VIX and the volatility factor is statistically significant. The jump intensity is also statedependent. We analyze the impact of jump factor on the VIX dynamics.

Suggested Citation

  • Xin Zang & Jun Ni & Jing-Zhi Huang & Lan Wu, 2015. "Double-jump stochastic volatility model for VIX: evidence from VVIX," Papers 1506.07554, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1506.07554
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1506.07554
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andreas Kaeck & Carol Alexander, 2010. "VIX Dynamics with Stochastic Volatility of Volatility," ICMA Centre Discussion Papers in Finance icma-dp2010-11, Henley Business School, University of Reading.
    2. Rama Cont & Thomas Kokholm, 2013. "A Consistent Pricing Model For Index Options And Volatility Derivatives," Post-Print hal-00801536, HAL.
    3. Bollerslev, Tim & Law, Tzuo Hann & Tauchen, George, 2008. "Risk, jumps, and diversification," Journal of Econometrics, Elsevier, vol. 144(1), pages 234-256, May.
    4. 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.
    5. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    6. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    7. Andrew Papanicolaou & Ronnie Sircar, 2014. "A regime-switching Heston model for VIX and S&P 500 implied volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1811-1827, October.
    8. San‐Lin Chung & Wei‐Che Tsai & Yaw‐Huei Wang & Pei‐Shih Weng, 2011. "The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(12), pages 1170-1201, December.
    9. Dimitris Psychoyios & George Dotsis & Raphael Markellos, 2010. "A jump diffusion model for VIX volatility options and futures," Review of Quantitative Finance and Accounting, Springer, vol. 35(3), pages 245-269, October.
    10. 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.
    11. Kaeck, Andreas & Alexander, Carol, 2013. "Continuous-time VIX dynamics: On the role of stochastic volatility of volatility," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 46-56.
    12. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    13. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    14. Bujar Huskaj & Marcus Nossman, 2013. "A Term Structure Model for VIX Futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(5), pages 421-442, May.
    15. 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.
    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. Xin Zang & Jun Ni & Jing-Zhi Huang & Lan Wu, 2017. "Double-jump diffusion model for VIX: evidence from VVIX," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 227-240, February.
    2. 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.
    3. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    4. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    5. 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.
    6. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    7. Bas Peeters, 2012. "Risk premiums in a simple market model for implied volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(5), pages 739-748, January.
    8. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    9. Jiling Cao & Xinfeng Ruan & Wenjun Zhang, 2020. "Inferring information from the S&P 500, CBOE VIX, and CBOE SKEW indices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 945-973, June.
    10. Kaeck, Andreas & Seeger, Norman J., 2020. "VIX derivatives, hedging and vol-of-vol risk," European Journal of Operational Research, Elsevier, vol. 283(2), pages 767-782.
    11. Andrew Papanicolaou & Ronnie Sircar, 2014. "A regime-switching Heston model for VIX and S&P 500 implied volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1811-1827, October.
    12. Lin, Yueh-Neng, 2013. "VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4432-4446.
    13. Bo Jing & Shenghong Li & Yong Ma, 2020. "Pricing VIX options with volatility clustering," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 928-944, June.
    14. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    15. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    16. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    17. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    18. 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.
    19. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
    20. Neumann, Maximilian & Prokopczuk, Marcel & Wese Simen, Chardin, 2016. "Jump and variance risk premia in the S&P 500," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 72-83.

    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:arx:papers:1506.07554. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.