IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1908.05419.html
   My bibliography  Save this paper

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

Author

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

Abstract

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, arXiv.org.
  • Handle: RePEc:arx:papers:1908.05419
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1908.05419
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christophe Chorro & Dominique Gu�gan & 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.
    2. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(2), pages 1-23, May.
    5. 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.
    6. 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.
    7. Jeffrey Chu & Stephen Chan & Saralees Nadarajah & Joerg Osterrieder, 2017. "GARCH Modelling of Cryptocurrencies," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(4), pages 1-15, October.
    8. 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.
    9. Bruder, Benjamin & Roncalli, Thierry, 2012. "Managing risk exposures using the risk budgeting approach," MPRA Paper 37246, University Library of Munich, Germany.
    10. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thilini Mahanama & Abootaleb Shirvani & Svetlozar T. Rachev, 2021. "Global Index on Financial Losses Due to Crime in the United States," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 14(7), pages 1-16, July.
    2. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2021. "Global Index on Financial Losses due to Crime in the United States," Papers 2105.03514, arXiv.org.

    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. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    2. 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).
    3. Gregor Dorfleitner & Carina Lung, 2018. "Cryptocurrencies from the perspective of euro investors: a re-examination of diversification benefits and a new day-of-the-week effect," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 472-494, December.
    4. Dean Fantazzini & Stephan Zimin, 2020. "A multivariate approach for the simultaneous modelling of market risk and credit risk for cryptocurrencies," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 47(1), pages 19-69, March.
    5. Corbet, Shaen & Cumming, Douglas J. & Lucey, Brian M. & Peat, Maurice & Vigne, Samuel A., 2020. "The destabilising effects of cryptocurrency cybercriminality," Economics Letters, Elsevier, vol. 191(C).
    6. Vahidin Jeleskovic & Mirko Meloni & Zahid Irshad Younas, 2020. "Cryptocurrencies: A Copula Based Approach for Asymmetric Risk Marginal Allocations," MAGKS Papers on Economics 202034, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    7. Aggarwal, Divya, 2019. "Do bitcoins follow a random walk model?," Research in Economics, Elsevier, vol. 73(1), pages 15-22.
    8. Gidea, Marian & Goldsmith, Daniel & Katz, Yuri & Roldan, Pablo & Shmalo, Yonah, 2020. "Topological recognition of critical transitions in time series of cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    9. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    10. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01244239, HAL.
    11. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    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. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Documents de travail du Centre d'Economie de la Sorbonne 15085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. 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.
    15. Bruno Ferreira Frascaroli, 2020. "Bitcoin's innovative aspects, return volatility and uncertainty shocks," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 7(3), pages 224-245.
    16. Kraaijeveld, Olivier & De Smedt, Johannes, 2020. "The predictive power of public Twitter sentiment for forecasting cryptocurrency prices," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 65(C).
    17. Samuel Asante Gyamerah, 2019. "Estimating the volatility of Bitcoin using GARCH models," Papers 1909.04903, arXiv.org, revised Oct 2019.
    18. 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.
    19. Roy Cerqueti & Massimiliano Giacalone & Raffaele Mattera, 2020. "Skewed non-Gaussian GARCH models for cryptocurrencies volatility modelling," Papers 2004.11674, arXiv.org.
    20. C. Y. Tan & Y. B. Koh & K. H. Ng & K. H. Ng, 2019. "Structural Change Analysis of Active Cryptocurrency Market," Papers 1909.10679, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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: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: . General contact details of provider: http://arxiv.org/ .

    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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.