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Pricing VXX option with default risk and positive volatility skew

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  • Bao, Qunfang
  • Li, Shenghong
  • Gong, Donggeng

Abstract

This paper proposes and makes a comparative study of alternative models for VXX option pricing. Factors such as mean-reversion, jumps, default risk and positive volatility skew are taken into consideration. In particular, default risk is characterized by jump-to-default framework and the “positive volatility skew” issue is addressed by stochastic volatility of volatility and jumps. Daily calibration is conducted and comparative study of the models is performed to check whether they properly fit market prices and generate reasonable positive volatility skews and deltas. Overall, jump-to-default extended LRJ model with positive correlated stochastic volatility (called JDLRJSV in the paper) serves as the best model in all the required aspects.

Suggested Citation

  • Bao, Qunfang & Li, Shenghong & Gong, Donggeng, 2012. "Pricing VXX option with default risk and positive volatility skew," European Journal of Operational Research, Elsevier, vol. 223(1), pages 246-255.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:246-255
    DOI: 10.1016/j.ejor.2012.06.006
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Sebastian A. Gehricke & Jin E. Zhang, 2018. "Modeling VXX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(8), pages 958-976, August.
    2. Kaeck, Andreas & Seeger, Norman J., 2020. "VIX derivatives, hedging and vol-of-vol risk," European Journal of Operational Research, Elsevier, vol. 283(2), pages 767-782.
    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. Da Fonseca, José, 2016. "On moment non-explosions for Wishart-based stochastic volatility models," European Journal of Operational Research, Elsevier, vol. 254(3), pages 889-894.
    5. Martino Grasselli & Andrea Mazzoran & Andrea Pallavicini, 2024. "A general framework for a joint calibration of VIX and VXX options," Annals of Operations Research, Springer, vol. 336(1), pages 3-26, May.
    6. 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.
    7. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    8. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options," Working Papers hal-01212018, HAL.
    9. Jiling Cao & Xinfeng Ruan & Shu Su & Wenjun Zhang, 2021. "Specification analysis of VXX option pricing models under Lévy processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(9), pages 1456-1477, September.
    10. Dias, José Carlos & Vidal Nunes, João Pedro, 2018. "Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral χ2 random variable," European Journal of Operational Research, Elsevier, vol. 265(2), pages 559-570.
    11. Liu, Yi-Fang & Zhang, Wei & Xu, Hai-Chuan, 2014. "Collective behavior and options volatility smile: An agent-based explanation," Economic Modelling, Elsevier, vol. 39(C), pages 232-239.
    12. 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.
    13. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    14. McGee, Richard J. & McGroarty, Frank, 2017. "The risk premium that never was: A fair value explanation of the volatility spread," European Journal of Operational Research, Elsevier, vol. 262(1), pages 370-380.

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