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Modeling VXX under jump diffusion with stochastic long‐term mean

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  • Sebastian A. Gehricke
  • Jin E. Zhang

Abstract

We develop a model for the VXX, the most actively traded VIX futures exchange‐traded note, using Duffie, Pan, and Singleton's affine jump diffusion framework, where the volatility process has jumps and a stochastic long‐term mean. We calibrate the model parameters using the VIX term structure data and show that our model provides the theoretical link between the VIX, VIX futures, and the VXX. Our model can be used for pricing VIX futures, the VXX and other short‐term VIX futures exchange‐traded products (ETPs). Our model could be extended to price options on the VXX and other short‐term VIX futures ETPs.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:10:p:1508-1534
    DOI: 10.1002/fut.22145
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    Cited by:

    1. Chen, Yu-Lun & Yang, J. Jimmy, 2021. "Trader positions in VIX futures," Journal of Empirical Finance, Elsevier, vol. 61(C), pages 1-17.
    2. Xiaoyu Tan & Chengxiang Wang & Wei Lin & Jin E. Zhang & Shenghong Li & Xuejun Zhao & Zili Zhang, 2021. "The term structure of the VXX option smirk: Pricing VXX option with a two‐factor model and asymmetry jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 439-457, April.
    3. 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.
    4. Gehricke, Sebastian A. & Zhang, Jin E., 2021. "Tracking performance of VIX futures ETPs," Journal of Empirical Finance, Elsevier, vol. 61(C), pages 103-117.
    5. Wei Lin & Jin E. Zhang, 2022. "Pricing VXX options by modeling VIX directly," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 888-922, May.

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