IDEAS home Printed from https://ideas.repec.org/a/kap/rqfnac/v59y2022i2d10.1007_s11156-022-01055-x.html
   My bibliography  Save this article

Stochastic properties and pricing of bitcoin using a GJR-GARCH model with conditional skewness and kurtosis components

Author

Listed:
  • Panayiotis Theodossiou

    (Cyprus University of Technology)

  • Polina Ellina

    (Cyprus University of Technology
    American University of Cyprus (AUCY))

  • Christos S. Savva

    (Cyprus University of Technology)

Abstract

Using a flexible statistical framework that accounts for time-varying skewness and leptokurtosis, we examine the stochastic behavior of Bitcoin in comparison to five major currencies. The empirical findings reveal that the distribution of all series is leptokurtic. Once the effect of skewness-kurtosis is considered, the true price of risk is obtained, with implications on policymakers’ and investors’ strategies.

Suggested Citation

  • Panayiotis Theodossiou & Polina Ellina & Christos S. Savva, 2022. "Stochastic properties and pricing of bitcoin using a GJR-GARCH model with conditional skewness and kurtosis components," Review of Quantitative Finance and Accounting, Springer, vol. 59(2), pages 695-716, August.
    • Handle: RePEc:kap:rqfnac:v:59:y:2022:i:2:d:10.1007_s11156-022-01055-x
    DOI: 10.1007/s11156-022-01055-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11156-022-01055-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11156-022-01055-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    2. Marie Briere & Kim Oosterlinck & Ariane Szafarz, 2015. "Virtual Currency, Tangible Return: Portfolio Diversification with Bitcoins," Post-Print CEB, ULB -- Universite Libre de Bruxelles, vol. 16(6), pages 365-373.
    3. Christian M Hafner, 2020. "Testing for Bubbles in Cryptocurrencies with Time-Varying Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 233-249.
    4. Panayiotis Theodossiou, 2015. "Skewed Generalized Error Distribution of Financial Assets and Option Pricing," Multinational Finance Journal, Multinational Finance Journal, vol. 19(4), pages 223-266, December.
    5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Corbet, Shaen & Meegan, Andrew & Larkin, Charles & Lucey, Brian & Yarovaya, Larisa, 2018. "Exploring the dynamic relationships between cryptocurrencies and other financial assets," Economics Letters, Elsevier, vol. 165(C), pages 28-34.
    8. Mazur Błażej & Pipień Mateusz, 2018. "Time-varying asymmetry and tail thickness in long series of daily financial returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-21, December.
    9. Christos S Savva & Panayiotis Theodossiou, 2018. "The Risk and Return Conundrum Explained: International Evidence," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 486-521.
    10. Joerg Osterrieder & Julian Lorenz, 2017. "A Statistical Risk Assessment Of Bitcoin And Its Extreme Tail Behavior," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-19, March.
    11. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    12. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    13. Guesmi, Khaled & Saadi, Samir & Abid, Ilyes & Ftiti, Zied, 2019. "Portfolio diversification with virtual currency: Evidence from bitcoin," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 431-437.
    14. Panayiotis Theodossiou & Christos S. Savva, 2016. "Skewness and the Relation Between Risk and Return," Management Science, INFORMS, vol. 62(6), pages 1598-1609, June.
    15. Frans de Roon & Paul Karehnke, 2017. "Addendum: A Simple Skewed Distribution with Asset Pricing Applications," Review of Finance, European Finance Association, vol. 21(6), pages 2401-2401.
    16. Theodossiou, Panayiotis, 1994. "The Stochastic Properties of Major Canadian Exchange Rates," The Financial Review, Eastern Finance Association, vol. 29(2), pages 193-221, May.
    17. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    18. Panayiotis Theodossiou & Dimitris Tsouknidis & Christos Savva, 2020. "Freight rates in downside and upside markets: pricing of own and spillover risks from other shipping segments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1097-1119, June.
    19. Baur, Dirk G. & Dimpfl, Thomas, 2018. "Asymmetric volatility in cryptocurrencies," Economics Letters, Elsevier, vol. 173(C), pages 148-151.
    20. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    21. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    22. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    23. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," JRFM, MDPI, vol. 10(4), pages 1-15, October.
    24. C. Baek & M. Elbeck, 2015. "Bitcoins as an investment or speculative vehicle? A first look," Applied Economics Letters, Taylor & Francis Journals, vol. 22(1), pages 30-34, January.
    25. Frans de Roon & Paul Karehnke, 2017. "A Simple Skewed Distribution with Asset Pricing Applications," Review of Finance, European Finance Association, vol. 21(6), pages 2169-2197.
    26. Akhtaruzzaman, Md & Sensoy, Ahmet & Corbet, Shaen, 2020. "The influence of Bitcoin on portfolio diversification and design," Finance Research Letters, Elsevier, vol. 37(C).
    27. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2013. "Modeling Market Downside Volatility," Review of Finance, European Finance Association, vol. 17(1), pages 443-481.
    28. Baur, Dirk G. & Hong, KiHoon & Lee, Adrian D., 2018. "Bitcoin: Medium of exchange or speculative assets?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 54(C), pages 177-189.
    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. Ioannidis, Filippos & Kosmidou, Kyriaki & Savva, Christos & Theodossiou, Panayiotis, 2021. "Electricity pricing using a periodic GARCH model with conditional skewness and kurtosis components," Energy Economics, Elsevier, vol. 95(C).
    2. Delis, Manthos D. & Savva, Christos S. & Theodossiou, Panayiotis, 2021. "The impact of the coronavirus crisis on the market price of risk," Journal of Financial Stability, Elsevier, vol. 53(C).
    3. Katsiampa, Paraskevi, 2019. "An empirical investigation of volatility dynamics in the cryptocurrency market," Research in International Business and Finance, Elsevier, vol. 50(C), pages 322-335.
    4. Panayiotis Theodossiou & Dimitris Tsouknidis & Christos Savva, 2020. "Freight rates in downside and upside markets: pricing of own and spillover risks from other shipping segments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1097-1119, June.
    5. Delis, Manthos & Savva, Christos & Theodossiou, Panayiotis, 2020. "A Coronavirus Asset Pricing Model: The Role of Skewness," MPRA Paper 100877, University Library of Munich, Germany.
    6. Kwon, Ji Ho, 2020. "Tail behavior of Bitcoin, the dollar, gold and the stock market index," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 67(C).
    7. 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.
    8. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    9. Ardia, David & Bluteau, Keven & Rüede, Maxime, 2019. "Regime changes in Bitcoin GARCH volatility dynamics," Finance Research Letters, Elsevier, vol. 29(C), pages 266-271.
    10. Aurelio F. Bariviera & Ignasi Merediz‐Solà, 2021. "Where Do We Stand In Cryptocurrencies Economic Research? A Survey Based On Hybrid Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 377-407, April.
    11. Ahmed, Walid M.A., 2020. "Is there a risk-return trade-off in cryptocurrency markets? The case of Bitcoin," Journal of Economics and Business, Elsevier, vol. 108(C).
    12. Andrea Flori, 2019. "Cryptocurrencies In Finance: Review And Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-22, August.
    13. Cristina Chinazzo & Vahidin Jeleskovic, 2024. "Forecasting Bitcoin Volatility: A Comparative Analysis of Volatility Approaches," Papers 2401.02049, arXiv.org.
    14. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    15. Haffar, Adlane & Le Fur, Éric, 2022. "Time-varying dependence of Bitcoin," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 211-220.
    16. Garcia-Jorcano, Laura & Benito, Sonia, 2020. "Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying," Research in International Business and Finance, Elsevier, vol. 54(C).
    17. López-Martín, Carmen & Arguedas-Sanz, Raquel & Muela, Sonia Benito, 2022. "A cryptocurrency empirical study focused on evaluating their distribution functions," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 387-407.
    18. Besma Hkiri & Juncal Cunado & Mehmet Balcilar & Rangan Gupta, 2021. "Time-varying relationship between conventional and unconventional monetary policies and risk aversion: international evidence from time- and frequency-domains," Empirical Economics, Springer, vol. 61(6), pages 2963-2983, December.
    19. Panagiotidis, Theodore & Stengos, Thanasis & Vravosinos, Orestis, 2019. "The effects of markets, uncertainty and search intensity on bitcoin returns," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 220-242.
    20. Walther, Thomas & Klein, Tony & Bouri, Elie, 2019. "Exogenous drivers of Bitcoin and Cryptocurrency volatility – A mixed data sampling approach to forecasting," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 63(C).

    More about this item

    Keywords

    Conditional skewness and kurtosis; Skewness price of risk; Upside and downside market probabilities; Skewed generalized error distribution;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    Statistics

    Access and download statistics

    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:kap:rqfnac:v:59:y:2022:i:2:d:10.1007_s11156-022-01055-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://springer.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.