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

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 Economics2016). 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.