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Pricing volatility options under stochastic skew with application to the VIX index

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  • Jacinto Marabel Romo

Abstract

In recent years, there has been a remarkable growth of volatility options. In particular, VIX options are among the most actively trading contracts at Chicago Board Options Exchange. These options exhibit upward sloping volatility skew and the shape of the skew is largely independent of the volatility level. To take into account these stylized facts, this article introduces a novel two-factor stochastic volatility model with mean reversion that accounts for stochastic skew consistent with empirical evidence. Importantly, the model is analytically tractable. In this sense, I solve the pricing problem corresponding to standard-start, as well as to forward-start European options through the Fast Fourier Transform. To illustrate the practical performance of the model, I calibrate the model parameters to the quoted prices of European options on the VIX index. The calibration results are fairly good indicating the ability of the model to capture the shape of the implied volatility skew associated with VIX options.

Suggested Citation

  • Jacinto Marabel Romo, 2017. "Pricing volatility options under stochastic skew with application to the VIX index," The European Journal of Finance, Taylor & Francis Journals, vol. 23(4), pages 353-374, March.
  • Handle: RePEc:taf:eurjfi:v:23:y:2017:i:4:p:353-374
    DOI: 10.1080/1351847X.2015.1092165
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    Cited by:

    1. 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.
    2. Natasha Latif & Shafqat Ali Shad & Muhammad Usman & Chandan Kumar & Bahman B Motii & MD Mahfuzer Rahman & Khuram Shafi & Zahra Idrees, 2023. "Pragmatic Comparison Analysis of Alternative Option Pricing Models," Papers 2309.09890, arXiv.org.
    3. Ouandlous, Arav & Barkoulas, John T. & Alhaj-Yaseen, Yaseen, 2018. "Persistence and discontinuity in the VIX dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 333-344.
    4. 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.

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