There are two fundamental contributions of this work. On the application side, one of the most challenging problems is tackled, predicting day-ahead crypto-currency prices. On the theoretical front, a new dynamical modeling approach is proposed. The proposed approach keeps the probabilistic formulation of the State-Space Model that yields point estimates along with the uncertainty about the estimate and the function approximation ability of the deep neural network. We call the proposed approach the deep state-space model. The experiments are carried out on established cryptocurrencies (obtained from Yahoo Finance). The goal of the work has been to predict the price for the next day. Benchmarking has been done with both state-of-the-art and classical dynamical modeling techniques. Results show that the proposed approach yields the best overall results in terms of accuracy.