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Options valuation and calibration for leveraged exchange-traded funds with Heston–Nandi and inverse Gaussian GARCH models

Author

Listed:
  • Hongkai Cao

    (School of Business, Stevens Institute of Technology, Hoboken, NJ 07030, United States)

  • Rupak Chatterjee

    (Department of Physics and Center for Quantum Science and Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, United States)

  • Zhenyu Cui

    (School of Business and Center for Quantum Science and Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, United States)

Abstract

Leveraged exchange-traded funds (LETF) are newly introduced ETFs that have become increasingly popular. It closely tracks the value of an underlying index while allowing for additional leverage. In this paper, we consider the valuation of options written on LETF under two popular affine GARCH models, the Heston–Nandi model and the inverse Gaussian GARCH model. We also calibrate the two models using market data, and demonstrate the superior pricing performance.

Suggested Citation

  • Hongkai Cao & Rupak Chatterjee & Zhenyu Cui, 2019. "Options valuation and calibration for leveraged exchange-traded funds with Heston–Nandi and inverse Gaussian GARCH models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 1-37, September.
    • Handle: RePEc:wsi:ijfexx:v:06:y:2019:i:03:n:s2424786319500270
    DOI: 10.1142/S2424786319500270
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    References listed on IDEAS

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    1. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
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    3. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
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    5. Xinglin Yang & Peng Wang, 2018. "VIX futures pricing with conditional skewness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1126-1151, September.
    6. Härdle, Wolfgang Karl & Nasekin, Sergey & Hong, Zhiwu, 2016. "Leveraged ETF options implied volatility paradox: A statistical study," SFB 649 Discussion Papers 2016-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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    8. Tim Leung & Matthew Lorig & Andrea Pascucci, 2014. "Leveraged {ETF} implied volatilities from {ETF} dynamics," Papers 1404.6792, arXiv.org, revised Apr 2015.
    9. Charupat, Narat & Miu, Peter, 2011. "The pricing and performance of leveraged exchange-traded funds," Journal of Banking & Finance, Elsevier, vol. 35(4), pages 966-977, April.
    10. Alexandru Badescu & Zhenyu Cui & Juan-Pablo Ortega, 2017. "Non-affine GARCH Option Pricing Models, Variance-Dependent Kernels, and Diffusion Limits," Journal of Financial Econometrics, Oxford University Press, vol. 15(4), pages 602-648.
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    Cited by:

    1. Hongkai Cao & Alexandru Badescu & Zhenyu Cui & Sarath Kumar Jayaraman, 2020. "Valuation of VIX and target volatility options with affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(12), pages 1880-1917, December.

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