Deposit and Withdrawal Dynamics: A Data-Based Mutually-Exciting Stochastic Model

Abstract

This paper proposes a mutually exciting discrete-time stochastic model to capture two essential features underlying the bank-customer behavior process---the dependence on the past behavior (i.e., path-dependence) and the behavioral interdependence between deposit and withdrawal activities (i.e., mutual excitation). In reality, despite the existence of large-scale data sources, the granular information contained in the data set can still be limited, for instance, aggregated versus individual activities. If the data are observed in an aggregated format, existing continuous-time models with mutually exciting and path-dependence features (e.g., a Hawkes-type model) cannot be directly applied. We thus propose a novel discrete-time stochastic model to tackle this practical and technical challenge. Despite the challenge, we are able to fully characterize the probability distribution for the customer deposit and withdrawal likelihood (i.e., the closed-form characteristic functions under the discrete-time setting), and hence we are able to theoretically quantify customer performance measures (i.e., churn probability, long-term average account value, and liquidity risk) and establish efficient maximum likelihood estimation. To validate the performance of our proposed model, we calibrate it with a customer deposit and withdrawal data set from one leading online money market fund. We compare our model with classic time-series and machine-learning models and show that our model is able to achieve high prediction accuracy. The theoretical tractability and predictive accuracy enable us to build optimization models for improving firm performance, and we illustrate one application through a personalized interest-rate optimization problem. On a broader note, our model framework is generally applicable to characterize any time-series data with path-dependence, mutual excitation, and aggregated observation (i.e., discrete-time) in nature, and to inform optimal policies for decision makers.