A Confidence-Based Model for Asset and Derivative Prices in the Bitcoin Market

We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices causing a Bubble effect, the presence of which is documented in several papers about the cryptocurrency. In this paper we develop a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as the behavior of a second factor affecting the price itself, which we name confidence indicator. The two dynamics are possibly correlated and we also take into account a delay between the confidence indicator and its delivered effect on the BitCoin price. Statistical properties of the suggested model are investigated and its arbitrage-free property is shown. Further, based on risk-neutral evaluation, a quasi-closed formula is derived for European style derivatives on the BitCoin. A short numerical application is finally provided.