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Pricing VIX derivatives with free stochastic volatility model

Author

Listed:
  • Wei Lin

    (Zhejiang University)

  • Shenghong Li

    (Zhejiang University)

  • Shane Chern

    (Pennsylvania State University)

  • Jin E. Zhang

    (University of Otago)

Abstract

This paper aims to develop a new free stochastic volatility model, joint with jumps. By freeing the power parameter of instantaneous variance, this paper takes Heston model and 3/2 model for special examples, and extends the generalizability. This model is named after free stochastic volatility model, and it owns two distinctive features. First of all, the power parameter is not constrained, so as to enable the data to voice its authentic direction. The Generalized Methods of Moments suggest that the purpose of this newly-added parameter is to create various volatility fluctuations observed in financial market. Secondly, even upward and downward jumps are separately modeled to accommodate the market data, this paper still provides the quasi-closed-form solutions for futures and option prices. Consequently, the model is novel and highly tractable. Here, it should be noted that the data on VIX futures and corresponding option contracts is employed to evaluate the model, in terms of its pricing and implied volatility features capturing performance. To sum up, the free stochastic volatility model with asymmetric jumps is capable of adequately capturing the implied volatility dynamics. Thus, it can be regarded as a model advantageous in pricing VIX derivatives with fixed power volatility models.

Suggested Citation

  • Wei Lin & Shenghong Li & Shane Chern & Jin E. Zhang, 2019. "Pricing VIX derivatives with free stochastic volatility model," Review of Derivatives Research, Springer, vol. 22(1), pages 41-75, April.
    • Handle: RePEc:kap:revdev:v:22:y:2019:i:1:d:10.1007_s11147-018-9145-y
    DOI: 10.1007/s11147-018-9145-y
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    References listed on IDEAS

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    Cited by:

    1. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.
    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. Qiang Liu & Yuhan Jiao & Shuxin Guo, 2022. "GARCH pricing and hedging of VIX options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(6), pages 1039-1066, June.

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    More about this item

    Keywords

    Free stochastic volatility; Jumps; VIX derivatives;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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