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Market attention and Bitcoin price modeling: theory, estimation and option pricing

Author

Listed:
  • Alessandra Cretarola

    (University of Perugia)

  • Gianna Figà-Talamanca

    (University of Perugia)

  • Marco Patacca

    (Léonard de Vinci Pôle Universitaire, Research Center
    University of Perugia)

Abstract

The goal of this paper is to provide a novel quantitative framework to describe the Bitcoin price behavior, estimate model parameters and study the pricing problem for Bitcoin derivatives. To this end, we propose a continuous time model for Bitcoin price motivated by the findings in recent literature on Bitcoin, showing that price changes are affected by sentiment and attention of investors, see e.g., (Kristoufek in Sci Rep 3:3415, 2013, PLoS ONE 10(4):e0123923, 2015; Bukovina and Marticek in Sentiment and bitcoin volatility. Technical report, Mendel University in Brno, Faculty of Business and Economics 2016). Economic studies, such as Yermack (Handbook of Digital Currency, chapter second. Elsevier, Amsterdam, pp 31–43, 2015), have also classified Bitcoin as a speculative asset rather than a currency due to its high volatility. Building on these outcomes, the price dynamics in our suggestion is indeed affected by an exogenous factor which represents market attention in the Bitcoin system. We prove the model to be arbitrage-free under a mild condition and we fit the model to historical data for the Bitcoin price; after obtaining a approximate formula for the likelihood, parameter values are estimated by means of the profile likelihood method. In addition, we derive a closed pricing formula for European-style derivatives on Bitcoin, the performance of which is assessed on a panel of market prices for Plain Vanilla options quoted on www.deribit.com .

Suggested Citation

  • Alessandra Cretarola & Gianna Figà-Talamanca & Marco Patacca, 2020. "Market attention and Bitcoin price modeling: theory, estimation and option pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 187-228, June.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:1:d:10.1007_s10203-019-00262-x
    DOI: 10.1007/s10203-019-00262-x
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Alessandra Cretarola & Gianna Figà-Talamanca & Cyril Grunspan, 2021. "Blockchain and cryptocurrencies: economic and financial research," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 781-787, December.
    2. Halousková, Martina & Stašek, Daniel & Horváth, Matúš, 2022. "The role of investor attention in global asset price variation during the invasion of Ukraine," Finance Research Letters, Elsevier, vol. 50(C).
    3. Gianna Figá-Talamanca & Sergio Focardi & Marco Patacca, 2021. "Common dynamic factors for cryptocurrencies and multiple pair-trading statistical arbitrages," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 863-882, December.
    4. Kuo-Shing Chen & Yu-Chuan Huang, 2021. "Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging," Mathematics, MDPI, vol. 9(20), pages 1-24, October.
    5. Ahmed, Walid M.A., 2022. "Robust drivers of Bitcoin price movements: An extreme bounds analysis," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    6. Carol Alexander & Ding Chen & Arben Imeraj, 2021. "Inverse and Quanto Inverse Options in a Black-Scholes World," Papers 2107.12041, arXiv.org, revised Oct 2022.

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    More about this item

    Keywords

    Bitcoin; Market attention; Stochastic models; Option pricing; Maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles

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