Market attention and Bitcoin price modeling: theory, estimation and option pricing. (English) Zbl 1444.91208
Summary: 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., [L. Kristoufek, “BitCoin meets Google trends and Wikipedia: quantifying the relationship between phenomena of the internet era”, Sci. Rep. 3, Article ID 3415, 7 p. (2013; doi:10.1038/srep03415); “What are the main drivers of the bitcoin price? Evidence from wavelet coherence analysis”, PLoS ONE 10, No. 4, Article Id e0123923, 15 p. (2015; doi:10.1371/journal.pone.0123923); J. Bukovina and M. Martiček, Sentiment and bitcoin volatility. Technical report. Brno: Mendel University Faculty of Business and Economics (2016)]. Economic studies, such as [D. Yermack, “Is Bitcoin a real currency?”, in: Handbook of digital currency. Amsterdam: Elsevier. 31–43 (2015; doi:10.1016/B978-0-12-802117-0.00002-3)], 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 http://www.deribit.com.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G99 | Actuarial science and mathematical finance |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 91B70 | Stochastic models in economics |
Keywords:
Bitcoin; market attention; stochastic models; option pricing; maximum likelihood estimationSoftware:
FinTSReferences:
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