IDEAS home Printed from
   My bibliography  Save this paper

Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation


  • Yuan Hu
  • Svetlozar T. Rache
  • Frank J. Fabozzi


Despite being described as a medium of exchange, cryptocurrencies do not have the typical attributes of a medium of exchange. Consequently, cryptocurrencies are more appropriately described as crypto assets. A common investment attribute shared by the more than 2,500 crypto assets is that they are highly volatile. An investor interested in reducing price volatility of a portfolio of crypto assets can do so by constructing an optimal portfolio through standard optimization techniques that minimize tail risk. Because crypto assets are not backed by any real assets, forming a hedge to reduce the risk contribution of a single crypto asset can only be done with another set of similar assets (i.e., a set of other crypto assets). A major finding of this paper is that crypto portfolios constructed via optimizations that minimize variance and Conditional Value at Risk outperform a major stock market index (the S$\&$P 500). As of this writing, options in which the underlying is a crypto asset index are not traded, one of the reasons being that the academic literature has not formulated an acceptable fair pricing model. We offer a fair valuation model for crypto asset options based on a dynamic pricing model for the underlying crypto assets. The model was carefully backtested and therefore offers a reliable model for the underlying crypto assets in the natural world. We then obtain the valuation of crypto options by passing the natural world to the equivalent martingale measure via the Esscher transform. Because of the absence of traded crypto options we could not compare the prices obtained from our valuation model to market prices. Yet, we can claim that if such options on crypto assets are introduced, they should follow closely our theoretical prices after adjusting for market frictions and design feature nuances.

Suggested Citation

  • Yuan Hu & Svetlozar T. Rache & Frank J. Fabozzi, 2019. "Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation," Papers 1908.05419,
  • Handle: RePEc:arx:papers:1908.05419

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    1. S. V. Stoyanov & S. T. Rachev & F. J. Fabozzi, 2007. "Optimal Financial Portfolios," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 401-436.
    2. Christophe Chorro & Dominique Guégan & Florian Ielpo, 2012. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1079-1094, April.
    3. repec:eee:ecmode:v:64:y:2017:i:c:p:74-81 is not listed on IDEAS
    4. Bruder, Benjamin & Roncalli, Thierry, 2012. "Managing risk exposures using the risk budgeting approach," MPRA Paper 37246, University Library of Munich, Germany.
    5. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. repec:gam:jjrfmx:v:10:y:2017:i:2:p:12-:d:100126 is not listed on IDEAS
    8. Asmerilda Hitaj & Lorenzo Mercuri, 2013. "Portfolio allocation using multivariate variance gamma models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 65-99, March.
    9. Balcilar, Mehmet & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2017. "Can volume predict Bitcoin returns and volatility? A quantiles-based approach," Economic Modelling, Elsevier, vol. 64(C), pages 74-81.
    10. repec:gam:jjrfmx:v:10:y:2017:i:4:p:17-:d:113895 is not listed on IDEAS
    11. S. R. Hurst & Eckhard Platen & S. T. Rachev, 1999. "Option pricing for a logstable asset price model," Published Paper Series 1999-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:arx:papers:1908.05419. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.