Is Bitcoin a bubble?

Abstract

The narrative of a Bitcoin is a bubble is very common. We employ statistical techniques to empirically evaluate such claim. A branch of literature links the existence of a bubble in some financial asset’s price to strict local martingales — a finitely lived asset has a bubble if, and only if, it is a strict local martingale under the equivalent risk-neutral measure. A diffusion process is a strict local martingale if its volatility increases faster than linearly as its level grows. We apply a nonparametric method to estimate the volatility function of Bitcoin daily and high frequency prices, as well as of more traditional financial assets. We then estimate the stochastic volatility model of Andersen and Piterbarg (2007), whose parameter space has a specific subset under which the asset’s price is a strict local martingale. Results suggest the existence of a bubble in Bitcoin prices from early 2013 to mid 2014, but, interestingly, not in late 2017.