  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.
