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Bitcoin option pricing with a SETAR-GARCH model

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  • Tak Kuen Siu
  • Robert J. Elliott

Abstract

This paper aims to study the pricing of Bitcoin options with a view to incorporating both conditional heteroscedasticity and regime switching in Bitcoin returns. Specifically, a nonlinear time series model combining both the self-exciting threshold autoregressive (SETAR) model and the generalized autoregressive conditional heteroscedastic (GARCH) model is adopted for modeling Bitcoin return dynamics. Specifically, the SETAR model is used to model regime switching and the Heston-Nandi GARCH model is adopted to model conditional heteroscedasticity. Both the conditional Esscher transform and the variance-dependent pricing kernel are used to specify pricing kernels. Numerical studies on the Bitcoin option prices using real bitcoins data are presented.

Suggested Citation

  • Tak Kuen Siu & Robert J. Elliott, 2021. "Bitcoin option pricing with a SETAR-GARCH model," The European Journal of Finance, Taylor & Francis Journals, vol. 27(6), pages 564-595, April.
    • Handle: RePEc:taf:eurjfi:v:27:y:2021:i:6:p:564-595
    DOI: 10.1080/1351847X.2020.1828962
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    Citations

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    Cited by:

    1. Alessandra Cretarola & Gianna Figà-Talamanca & Cyril Grunspan, 2021. "Blockchain and cryptocurrencies: economic and financial research," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 781-787, December.
    2. D’Amato, Valeria & Levantesi, Susanna & Piscopo, Gabriella, 2022. "Deep learning in predicting cryptocurrency volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    3. F. Leung & M. Law & S. K. Djeng, 2024. "Deterministic modelling of implied volatility in cryptocurrency options with underlying multiple resolution momentum indicator and non-linear machine learning regression algorithm," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-25, December.
    4. Ao Shu & Feiyang Cheng & Jianlei Han & Zini Liang & Zheyao Pan, 2023. "Arbitrage across different Bitcoin exchange venues: Perspectives from investor base and market related events," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 63(5), pages 5183-5210, December.
    5. Brini, Alessio & Lenz, Jimmie, 2024. "Pricing cryptocurrency options with machine learning regression for handling market volatility," Economic Modelling, Elsevier, vol. 136(C).
    6. Kuo-Shing Chen & Yu-Chuan Huang, 2021. "Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging," Mathematics, MDPI, vol. 9(20), pages 1-24, October.
    7. Alexander, Carol & Deng, Jun & Feng, Jianfen & Wan, Huning, 2023. "Net buying pressure and the information in bitcoin option trades," Journal of Financial Markets, Elsevier, vol. 63(C).
    8. Rico-Peña, Juan Jesús & Arguedas-Sanz, Raquel & López-Martin, Carmen, 2023. "Models used to characterise blockchain features. A systematic literature review and bibliometric analysis," Technovation, Elsevier, vol. 123(C).
    9. Tak Kuen Siu, 2024. "Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty," JRFM, MDPI, vol. 17(10), pages 1-32, September.
    10. Pierre J. Venter & Eben Maré, 2021. "Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing," JRFM, MDPI, vol. 14(6), pages 1-14, June.
    11. Elisa Al`os & Eulalia Nualart & Makar Pravosud, 2023. "On the implied volatility of Inverse options under stochastic volatility models," Papers 2401.00539, arXiv.org, revised Sep 2024.
    12. Tak Kuen Siu, 2023. "Bayesian nonlinear expectation for time series modelling and its application to Bitcoin," Empirical Economics, Springer, vol. 64(1), pages 505-537, January.
    13. Carol Alexander & Ding Chen & Arben Imeraj, 2021. "Inverse and Quanto Inverse Options in a Black-Scholes World," Papers 2107.12041, arXiv.org, revised Oct 2022.

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