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GARCH Generated Volatility Indices of Bitcoin and CRIX

Author

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  • Pierre J. Venter

    (Department of Actuarial Science, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa
    Department of Finance and Investment Management, University of Johannesburg, P.O. Box 524, Aucklandpark 2006, South Africa)

  • Eben Maré

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa)

Abstract

In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset.

Suggested Citation

  • Pierre J. Venter & Eben Maré, 2020. "GARCH Generated Volatility Indices of Bitcoin and CRIX," JRFM, MDPI, vol. 13(6), pages 1-15, June.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:6:p:121-:d:370116
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    References listed on IDEAS

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    Cited by:

    1. Bilel Sanhaji & Julien Chevallier, 2023. "Tracking ‘Pure’ Systematic Risk with Realized Betas for Bitcoin and Ethereum," Econometrics, MDPI, vol. 11(3), pages 1-36, August.
    2. 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.
    3. Abootaleb Shirvani & Stefan Mittnik & William Brent Lindquist & Svetlozar Rachev, 2024. "Bitcoin Volatility and Intrinsic Time Using Double-Subordinated Lévy Processes," Risks, MDPI, vol. 12(5), pages 1-21, May.
    4. Yin, Libo & Nie, Jing & Han, Liyan, 2021. "Understanding cryptocurrency volatility: The role of oil market shocks," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 233-253.
    5. Thanasis Stengos, 2021. "Recent Developments in Cryptocurrency Markets: Co-Movements, Spillovers and Forecasting," JRFM, MDPI, vol. 14(3), pages 1-3, February.
    6. Abootaleb Shirvani & Stefan Mittnik & W. Brent Lindquist & Svetlozar T. Rachev, 2021. "Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes," Papers 2109.15051, arXiv.org, revised Aug 2023.
    7. Klender Cortez & Martha del Pilar Rodríguez-García & Samuel Mongrut, 2020. "Exchange Market Liquidity Prediction with the K-Nearest Neighbor Approach: Crypto vs. Fiat Currencies," Mathematics, MDPI, vol. 9(1), pages 1-15, December.

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