The accurate comprehension of the risk drivers of different depository institutions is the key to their sustainable operation. In this paper, we analyze two stochastic approaches to model Non-Maturing Assets (NMAs) employing an Ornstein–Uhlenbeck process that can be used for the evaluation of the liquidity and interest risk of savings accounts in banks. We detail the models’ specifications, parameters, and simulation results. Furthermore, we examine the regular patterns, throughout the year, of the behavior of the volume of deposits into saving accounts in Colombia, in line with the results of other researchers in different countries. Finally, we found that a trend term should be incorporated into the model to capture the growth of the series.