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.

中文翻译：

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市场关注和比特币价格建模：理论，估计和期权定价

在最近的文献中，人们声称比特币的价格波动性比股票货币更容易波动，而且其价格的变化受关于比特币系统本身的情绪的影响。在Kristoufek [10]中，作者分析了基于交易以及基于受欢迎度的比特币价格潜在驱动因素，从而找到了积极的证据。在这里，我们认可这一发现，并在连续时间内考虑一个双变量模型来描述一个比特币的价格动态以及影响价格本身的第二个因素，这代表了一种情绪指标。我们证明了建议的模型在温和的条件下是无套利的，并且基于风险中性评估，我们获得了一个封闭的公式来近似欧洲风格衍生产品在BitCoin上的价格。通过对双变量过程的离散样本的联合可能性应用相同的近似技术，我们还能够使模型适合市场数据。这是通过将Google搜索量和Google搜索次数作为情感因素的可能替代值来完成的。此外，定价公式的性能是根据deribit.com网站获得的市场期权价格样本进行评估的。