IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2309.08175.html
   My bibliography  Save this paper

A Markovian empirical model for the VIX index and the pricing of the corresponding derivatives

Author

Listed:
  • Ying-Li Wang
  • Cheng-Long Xu
  • Ping He

Abstract

In this paper, we propose an empirical model for the VIX index. Our findings indicate that the VIX has a long-term empirical distribution. To model its dynamics, we utilize a continuous-time Markov process with a uniform distribution as its invariant distribution and a suitable function $h$. We determined that $h$ is the inverse function of the VIX data's empirical distribution. Additionally, we use the method of variables of separation to get the exact solution to the pricing problem for VIX futures and call options.

Suggested Citation

  • Ying-Li Wang & Cheng-Long Xu & Ping He, 2023. "A Markovian empirical model for the VIX index and the pricing of the corresponding derivatives," Papers 2309.08175, arXiv.org.
    • Handle: RePEc:arx:papers:2309.08175
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2309.08175
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jan Baldeaux & Alexander Badran, 2014. "Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 299-312, September.
    2. Andrew Papanicolaou, 2018. "Consistent Time-Homogeneous Modeling of SPX and VIX Derivatives," Papers 1812.05859, arXiv.org, revised Mar 2022.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. M. Avellaneda & A. Papanicolaou, 2019. "Statistics Of Vix Futures And Applications To Trading Volatility Exchange-Traded Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-30, February.
    5. Gabriel Drimus & Walter Farkas, 2013. "Local volatility of volatility for the VIX market," Review of Derivatives Research, Springer, vol. 16(3), pages 267-293, October.
    6. Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 Plus Jumps Model," Research Paper Series 306, Quantitative Finance Research Centre, University of Technology, Sydney.
    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. Andrew Papanicolaou, 2022. "Consistent time‐homogeneous modeling of SPX and VIX derivatives," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 907-940, July.
    2. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    3. Cao, Jiling & Kim, Jeong-Hoon & Liu, Wenqiang & Zhang, Wenjun, 2023. "Rescaling the double-mean-reverting 4/2 stochastic volatility model for derivative pricing," Finance Research Letters, Elsevier, vol. 58(PB).
    4. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    5. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    6. Liexin Cheng & Xue Cheng & Xianhua Peng, 2024. "Joint Calibration to SPX and VIX Derivative Markets with Composite Change of Time Models," Papers 2404.16295, arXiv.org, revised Aug 2024.
    7. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    8. Kailin Ding & Zhenyu Cui & Yanchu Liu, 2023. "Sequential Itô–Taylor expansions and characteristic functions of stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(12), pages 1750-1769, December.
    9. J.-P. Fouque & Y. F. Saporito, 2018. "Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 1003-1016, June.
    10. Andrew Papanicolaou, 2018. "Consistent Time-Homogeneous Modeling of SPX and VIX Derivatives," Papers 1812.05859, arXiv.org, revised Mar 2022.
    11. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    12. Wei Lin & Shenghong Li & Xingguo Luo & Shane Chern, 2015. "Consistent Pricing of VIX and Equity Derivatives with the 4/2 Stochastic Volatility Plus Jumps Model," Papers 1510.01172, arXiv.org, revised Nov 2015.
    13. Alexander Badran & Beniamin Goldys, 2015. "A Market Model for VIX Futures," Papers 1504.00428, arXiv.org.
    14. Wendong Zheng & Pingping Zeng, 2015. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Papers 1504.08136, arXiv.org.
    15. Wendong Zheng & Pingping Zeng, 2016. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 344-373, September.
    16. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching stochastic volatility model: estimation and calibration to VIX options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(1), pages 38-75, January.
    17. 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.
    18. Daniel Guterding, 2020. "Inventory effects on the price dynamics of VSTOXX futures quantified via machine learning," Papers 2002.08207, arXiv.org.
    19. Elisa Al`os & David Garc'ia-Lorite & Aitor Muguruza, 2018. "On smile properties of volatility derivatives and exotic products: understanding the VIX skew," Papers 1808.03610, arXiv.org.
    20. Lech A. Grzelak, 2022. "On Randomization of Affine Diffusion Processes with Application to Pricing of Options on VIX and S&P 500," Papers 2208.12518, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2309.08175. 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.