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Non-affine GARCH Option Pricing Models, Variance-Dependent Kernels, and Diffusion Limits

Author

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  • Alexandru Badescu
  • Zhenyu Cui
  • Juan-Pablo Ortega

Abstract

This paper investigates the pricing and weak convergence of an asymmetric non-affine, non-Gaussian GARCH model when the risk neutralization is based on a variance-dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a general setting and its weak limit is derived. We show how several GARCH diffusions, martingalized via well-known pricing kernels, are obtained as special cases and we derive necessary and sufficient conditions for the presence of financial bubbles. An extensive empirical analysis using both historical returns and options data illustrates the advantage of coupling this pricing kernel with non-Gaussian innovations.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:jfinec:v:15:y:2017:i:4:p:602-648.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbx022
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    Citations

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    Cited by:

    1. Badescu, Alexandru & Quaye, Enoch & Tunaru, Radu, 2022. "On non-negative equity guarantee calculations with macroeconomic variables related to house prices," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 119-138.
    2. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2019. "A general framework for time-changed Markov processes and applications," European Journal of Operational Research, Elsevier, vol. 273(2), pages 785-800.
    3. 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.
    4. Alexandru Badescu & Zhenyu Cui & Juan-Pablo Ortega, 2019. "Closed-form variance swap prices under general affine GARCH models and their continuous-time limits," Annals of Operations Research, Springer, vol. 282(1), pages 27-57, November.
    5. 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.
    6. Zhiyuan Pan & Yudong Wang & Li Liu & Qing Wang, 2019. "Improving volatility prediction and option valuation using VIX information: A volatility spillover GARCH model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 744-776, June.
    7. Tong, Chen, 2024. "Pricing CBOE VIX in non-affine GARCH models with variance risk premium," Finance Research Letters, Elsevier, vol. 62(PA).
    8. Maciej Augustyniak & Alexandru Badescu, 2021. "On the computation of hedging strategies in affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 710-735, May.
    9. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.

    More about this item

    Keywords

    bivariate diffusion limit; exponential linear variance-dependent pricing kernel; non-affine GARCH models; non-Gaussian innovations; option pricing;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • 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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