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A sentiment-based model for the BitCoin: theory, estimation and option pricing

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  • Alessandra Cretarola
  • Gianna Fig`a-Talamanca
  • Marco Patacca

Abstract

In recent literature it is claimed that BitCoin price behaves more likely to a volatile stock asset than a currency and that changes in its price are influenced by sentiment about the BitCoin system itself; in Kristoufek [10] the author analyses transaction based as well as popularity based potential drivers of the BitCoin price finding positive evidence. Here, we endorse this finding and consider a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as a second factor, affecting the price itself, which represents a sentiment indicator. We prove that the suggested model is arbitrage-free under a mild condition and, based on risk-neutral evaluation, we obtain a closed formula to approximate the price of European style derivatives on the BitCoin. By applying the same approximation technique to the joint likelihood of a discrete sample of the bivariate process, we are also able to fit the model to market data. This is done by using both the Volume and the number of Google searches as possible proxies for the sentiment factor. Further, the performance of the pricing formula is assessed on a sample of market option prices obtained by the website deribit.com.

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  • Alessandra Cretarola & Gianna Fig`a-Talamanca & Marco Patacca, 2017. "A sentiment-based model for the BitCoin: theory, estimation and option pricing," Papers 1709.08621, arXiv.org.
    • Handle: RePEc:arx:papers:1709.08621
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Ladislav Kristoufek, 2015. "What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-15, April.
    3. repec:men:wpaper:58_2015 is not listed on IDEAS
    4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    5. Jaroslav Bukovina & Matus Marticek, 2016. "Sentiment and Bitcoin Volatility," MENDELU Working Papers in Business and Economics 2016-58, Mendel University in Brno, Faculty of Business and Economics.
    6. Moshe Arye Milevsky & Steven E. Posner, 1999. "Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 7, pages 203-218, World Scientific Publishing Co. Pte. Ltd..
    7. Young Bin Kim & Sang Hyeok Lee & Shin Jin Kang & Myung Jin Choi & Jung Lee & Chang Hun Kim, 2015. "Virtual World Currency Value Fluctuation Prediction System Based on User Sentiment Analysis," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-18, August.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. David Yermack, 2013. "Is Bitcoin a Real Currency? An economic appraisal," NBER Working Papers 19747, National Bureau of Economic Research, Inc.
    10. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    11. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Lyócsa, Štefan & Molnár, Peter & Plíhal, Tomáš & Širaňová, Mária, 2020. "Impact of macroeconomic news, regulation and hacking exchange markets on the volatility of bitcoin," Journal of Economic Dynamics and Control, Elsevier, vol. 119(C).
    2. Wolfgang Karl Hardle & Campbell R. Harvey & Raphael C. G. Reule, 2020. "Editorial: Understanding Cryptocurrencies," Papers 2007.14702, arXiv.org.
    3. Adam Hayes, 2018. "Bitcoin price and its marginal cost of production: support for a fundamental value," Papers 1805.07610, arXiv.org.
    4. Wolfgang Karl Härdle & Campbell R Harvey & Raphael C G Reule, 2020. "Understanding Cryptocurrencies," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 181-208.
    5. Goodell, John W. & Alon, Ilan & Chiaramonte, Laura & Dreassi, Alberto & Paltrinieri, Andrea & Piserà, Stefano, 2023. "Risk substitution in cryptocurrencies: Evidence from BRICS announcements," Emerging Markets Review, Elsevier, vol. 54(C).

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