A novel dynamical model for the study of operational risk in banks is proposed. The equation of motion takes into account the interactions among different bank's processes, the spontaneous generation of losses via a noise term and the efforts made by the banks to avoid their occurrence. A scheme … for the estimation of some parameters of the model is illustrated, so that it can be tailored on the internal organizational structure of a specific bank. We focus on the case in which there are no causal loops in the matrix of couplings and exploit the exact solution to estimate also the parameters of the noise. The scheme for the estimation of the parameters is proved to be consistent and the model is shown to exhibit a remarkable capability in forecasting future cumulative losses.