IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v14y2021i6p261-d572373.html
   My bibliography  Save this article

Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing

Author

Listed:
  • 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
    These authors contributed equally to this work.)

  • Eben Maré

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa
    These authors contributed equally to this work.)

Abstract

In this paper, the Heston–Nandi futures option pricing model is applied to Bitcoin futures options. The model prices are compared to market prices to give an indication of the pricing performance. In addition, a multivariate Bitcoin futures option pricing methodology based on a multivatiate GARCH model is developed. The empirical results show that a symmetric model is a better fit when applied to Bitcoin futures returns, and also produces more accurate option prices compared to market prices for two out of three expiry dates considered.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:6:p:261-:d:572373
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/14/6/261/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/14/6/261/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pierre J. Venter & Eben Mare & Edson Pindza & David McMillan, 2020. "Price discovery in the cryptocurrency option market: A univariate GARCH approach," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1803524-180, January.
    2. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    3. Fang, Libing & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2019. "Does global economic uncertainty matter for the volatility and hedging effectiveness of Bitcoin?," International Review of Financial Analysis, Elsevier, vol. 61(C), pages 29-36.
    4. Dirk G. Baur & Brian M. Lucey, 2010. "Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold," The Financial Review, Eastern Finance Association, vol. 45(2), pages 217-229, May.
    5. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
    6. Rebecca Abraham, 2020. "The role of investor sentiment in the valuation of bitcoin and bitcoin derivatives," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 7(3), pages 203-223.
    7. Fassas, Athanasios P. & Papadamou, Stephanos & Koulis, Alexandros, 2020. "Price discovery in bitcoin futures," Research in International Business and Finance, Elsevier, vol. 52(C).
    8. Christian Conrad & Anessa Custovic & Eric Ghysels, 2018. "Long- and Short-Term Cryptocurrency Volatility Components: A GARCH-MIDAS Analysis," JRFM, MDPI, vol. 11(2), pages 1-12, May.
    9. Akanksha Jalan & Roman Matkovskyy & Saqib Aziz, 2021. "The Bitcoin options market: A first look at pricing and risk," Applied Economics, Taylor & Francis Journals, vol. 53(17), pages 2026-2041, April.
    10. Duan, Jin-Chuan & Pliska, Stanley R., 2004. "Option valuation with co-integrated asset prices," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 727-754, January.
    11. Alexander, Carol & Heck, Daniel F., 2020. "Price discovery in Bitcoin: The impact of unregulated markets," Journal of Financial Stability, Elsevier, vol. 50(C).
    12. Mahringer, Steffen & Prokopczuk, Marcel, 2015. "An empirical model comparison for valuing crack spread options," Energy Economics, Elsevier, vol. 51(C), pages 177-187.
    13. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    14. 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.
    15. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    16. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    17. Pierre J. Venter & Eben Maré, 2020. "GARCH Generated Volatility Indices of Bitcoin and CRIX," JRFM, MDPI, vol. 13(6), pages 1-15, June.
    18. Tianyi Wang & Yiwen Shen & Yueting Jiang & Zhuo Huang, 2017. "Pricing the CBOE VIX Futures with the Heston–Nandi GARCH Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(7), pages 641-659, July.
    19. Shahzad, Syed Jawad Hussain & Bouri, Elie & Roubaud, David & Kristoufek, Ladislav & Lucey, Brian, 2019. "Is Bitcoin a better safe-haven investment than gold and commodities?," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 322-330.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paolella, Marc S. & Polak, Paweł, 2015. "COMFORT: A common market factor non-Gaussian returns model," Journal of Econometrics, Elsevier, vol. 187(2), pages 593-605.
    2. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
    3. Wang, Qi & Wang, Zerong, 2020. "VIX valuation and its futures pricing through a generalized affine realized volatility model with hidden components and jump," Journal of Banking & Finance, Elsevier, vol. 116(C).
    4. Didik Susilo & Sugeng Wahyudi & Irene Rini Demi Pangestuti & Bayu Adi Nugroho & Robiyanto Robiyanto, 2020. "Cryptocurrencies: Hedging Opportunities From Domestic Perspectives in Southeast Asia Emerging Markets," SAGE Open, , vol. 10(4), pages 21582440209, November.
    5. Rubaiyat Ahsan Bhuiyan & Afzol Husain & Changyong Zhang, 2023. "Diversification evidence of bitcoin and gold from wavelet analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-36, December.
    6. 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.
    7. Bouri, Elie & Lucey, Brian & Roubaud, David, 2020. "Cryptocurrencies and the downside risk in equity investments," Finance Research Letters, Elsevier, vol. 33(C).
    8. Giacomo di Tollo & Joseph Andria & Gianni Filograsso, 2023. "The Predictive Power of Social Media Sentiment: Evidence from Cryptocurrencies and Stock Markets Using NLP and Stochastic ANNs," Mathematics, MDPI, vol. 11(16), pages 1-18, August.
    9. Venter, Pierre J & Maré, Eben, 2022. "Price discovery in the volatility index option market: A univariate GARCH approach," Finance Research Letters, Elsevier, vol. 44(C).
    10. Dimitrios Koutmos & Timothy King & Constantin Zopounidis, 2021. "Hedging uncertainty with cryptocurrencies: Is bitcoin your best bet?," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 44(4), pages 815-837, December.
    11. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    12. Klein, Tony & Pham Thu, Hien & Walther, Thomas, 2018. "Bitcoin is not the New Gold – A comparison of volatility, correlation, and portfolio performance," International Review of Financial Analysis, Elsevier, vol. 59(C), pages 105-116.
    13. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    14. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    15. Conlon, Thomas & Corbet, Shaen & McGee, Richard J., 2020. "Are cryptocurrencies a safe haven for equity markets? An international perspective from the COVID-19 pandemic," Research in International Business and Finance, Elsevier, vol. 54(C).
    16. Ángeles Cebrián-Hernández & Enrique Jiménez-Rodríguez, 2021. "Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    17. 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.
    18. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2020. "Affine multivariate GARCH models," Journal of Banking & Finance, Elsevier, vol. 118(C).
    19. Wüstenfeld, Jan & Geldner, Teo, 2022. "Economic uncertainty and national bitcoin trading activity," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    20. Ben Nouir, Jihed & Ben Haj Hamida, Hayet, 2023. "How do economic policy uncertainty and geopolitical risk drive Bitcoin volatility?," Research in International Business and Finance, Elsevier, vol. 64(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jjrfmx:v:14:y:2021:i:6:p:261-:d:572373. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.