We propose a doubly subordinated Lévy process, the normal double inverse Gaussian (NDIG), to model the time series properties of the cryptocurrency bitcoin. By using two subordinated processes, NDIG captures both the skew and fat-tailed properties of, as well as the intrinsic time driving,...

This paper constructs a class of multivariate Gaussian marked Poisson processes to model asset returns. The model proposed accommodates the cross section properties of trades, allows for returns to be correlated conditional on trading activity, and preserves the economic intuition of normality...