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The Skewness Implied in the Heston Model and Its Application

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  • Jin E. Zhang
  • Fang Zhen
  • Xiaoxia Sun
  • Huimin Zhao

Abstract

In this paper, we provide an exact formula for the skewness of stock returns implied in the Heston (1993) model by using a moment‐computing approach. We compute the moments of It o ˆ integrals by using It o ˆ 's Lemma skillfully. The model's affine property allows us to obtain analytical formulas for cumulants. The formulas for the variance and the third cumulant are written as time‐weighted sums of expected instantaneous variance, which are neater and more intuitive than those obtained with the characteristic function approach. Our skewness formula is then applied in calibrating Heston's model by using the market data of the CBOE VIX and SKEW. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:211–237, 2017

Suggested Citation

  • Jin E. Zhang & Fang Zhen & Xiaoxia Sun & Huimin Zhao, 2017. "The Skewness Implied in the Heston Model and Its Application," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(3), pages 211-237, March.
    • Handle: RePEc:wly:jfutmk:v:37:y:2017:i:3:p:211-237
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    Cited by:

    1. Wenli Zhu & Xinfeng Ruan, 2019. "Pricing Swaps on Discrete Realized Higher Moments Under the Lévy Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 507-532, February.
    2. Recchioni, Maria Cristina & Iori, Giulia & Tedeschi, Gabriele & Ouellette, Michelle S., 2021. "The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications," European Journal of Operational Research, Elsevier, vol. 293(1), pages 336-360.
    3. 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.
    4. Ostap Okhrin & Michael Rockinger & Manuel Schmid, 2023. "Distributional properties of continuous time processes: from CIR to bates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 397-419, September.
    5. Mora-Valencia, Andrés & Rodríguez-Raga, Santiago & Vanegas, Esteban, 2021. "Skew index: Descriptive analysis, predictive power, and short-term forecast," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    6. Pakorn Aschakulporn & Jin E. Zhang, 2022. "Bakshi, Kapadia, and Madan (2003) risk‐neutral moment estimators: An affine jump‐diffusion approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 365-388, March.
    7. Zhen, Fang, 2020. "Asymmetric signals and skewness," Economic Modelling, Elsevier, vol. 90(C), pages 32-42.
    8. Zhen Fang & Zhang Jin E., 2020. "Dissecting skewness under affine jump-diffusions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(4), pages 1-19, September.
    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.

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