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Non-linear volatility with normal inverse Gaussian innovations: ad-hoc analytic option pricing

Author

Listed:
  • Sharif Mozumder

    (University of Dhaka)

  • Bakhtear Talukdar

    (Department of Finance and Business Law, University of Wisconsin-Whitewater)

  • M. Humayun Kabir

    (Massey University Business School)

  • Bingxin Li

    (West Virginia University)

Abstract

This paper proposes an approximate closed-form option-pricing model based on a non-linear GARCH process with Normal Inverse Gaussian (NIG) Lévy innovations. We develop the mathematical framework and demonstrate how to obtain a closed-form solution to the option price when the return dynamics are characterized by NIG innovations for volatility that follow a non-linear GARCH process. Using a sample of S&P 500 index options, we calibrate the proposed model alongside popular existing models. Overall, from a unified comparison of various analytic pricing approaches, we find that our model performs significantly better than existing models, both in-sample and out-of-sample.

Suggested Citation

  • Sharif Mozumder & Bakhtear Talukdar & M. Humayun Kabir & Bingxin Li, 2024. "Non-linear volatility with normal inverse Gaussian innovations: ad-hoc analytic option pricing," Review of Quantitative Finance and Accounting, Springer, vol. 62(1), pages 97-133, January.
    • Handle: RePEc:kap:rqfnac:v:62:y:2024:i:1:d:10.1007_s11156-023-01195-8
    DOI: 10.1007/s11156-023-01195-8
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    References listed on IDEAS

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    More about this item

    Keywords

    Lévy innovations; Stochastic volatility; GARCH; Calibration; NIG;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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