IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v17y2017i2p227-240.html
   My bibliography  Save this article

Double-jump diffusion model for VIX: evidence from VVIX

Author

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

Abstract

This 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 jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyse the impact of the jump factor on VIX dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:2:p:227-240
    DOI: 10.1080/14697688.2016.1159318
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2016.1159318
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2016.1159318?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Viktor Todorov & George Tauchen, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 356-371, July.
    4. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    5. 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.
    6. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    7. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2012. "Stochastic Volatility of Volatility and Variance Risk Premia," Journal of Financial Econometrics, Oxford University Press, vol. 11(1), pages 1-46, December.
    8. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    9. 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.
    10. Bollerslev, Tim & Law, Tzuo Hann & Tauchen, George, 2008. "Risk, jumps, and diversification," Journal of Econometrics, Elsevier, vol. 144(1), pages 234-256, May.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peixuan Yuan, 2022. "Time-Varying Skew in VIX Derivatives Pricing," Management Science, INFORMS, vol. 68(10), pages 7761-7791, October.
    2. Barletta, Andrea & Santucci de Magistris, Paolo & Violante, Francesco, 2019. "A non-structural investigation of VIX risk neutral density," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 1-20.
    3. Hsu, Chih-Hsiang & Lee, Hsiu-Chuan & Lien, Donald, 2020. "Stock market uncertainty, volatility connectedness of financial institutions, and stock-bond return correlations," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 600-621.
    4. Gaoxiu Qiao & Gongyue Jiang, 2023. "VIX futures pricing based on high‐frequency VIX: A hybrid approach combining SVR with parametric models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(9), pages 1238-1260, September.
    5. Albers, Stefan, 2023. "The fear of fear in the US stock market: Changing characteristics of the VVIX," Finance Research Letters, Elsevier, vol. 55(PA).
    6. Gongyue Jiang & Gaoxiu Qiao & Feng Ma & Lu Wang, 2022. "Directly pricing VIX futures with observable dynamic jumps based on high‐frequency VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1518-1548, August.
    7. Fangsheng Yin & Yang Bian & Tianyi Wang, 2021. "A short cut: Directly pricing VIX futures with discrete‐time long memory model and asymmetric jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 458-477, April.

    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, 2015. "Double-jump stochastic volatility model for VIX: evidence from VVIX," Papers 1506.07554, arXiv.org, revised Jul 2015.
    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. 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.
    4. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    5. 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.
    6. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    7. Xinglin Yang & Ji Chen, 2021. "VIX term structure: The role of jump propagation risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 785-810, June.
    8. Ruan, Xinfeng & Zhang, Jin E., 2018. "Equilibrium variance risk premium in a cost-free production economy," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 42-60.
    9. Kaeck, Andreas, 2013. "Asymmetry in the jump-size distribution of the S&P 500: Evidence from equity and option markets," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1872-1888.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.

    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:taf:quantf:v:17:y:2017:i:2:p:227-240. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.