Quantifying Endogeneity of Cryptocurrency Markets

In this paper we construct a “reflexivity” index for Bitcoin cryptocurrency that measures the amount of activity generated endogenously within the market. For this purpose we fit a univariate self-exciting Hawkes process with two-classes of parametric kernels to high-frequency trade data. Its parsimonious representation of endogenous and exogenous dynamics allows for a direct comparison with tradi- tional asset classes in terms of the branching ratio. Furthermore, we formulate a Hawkes disorder problem, a variation to the Poisson disorder problem, and provide a simulation based solution for determining the optimal observation horizon. The paper concludes that mid-price dynamics of Bitcoin feature long-memory proper- ties, exceptionally well explained by the power-law kernel, and operate on a similar criticality level to currency markets.