Modelling the Bank Customer Activity Duration Based on the Cox Econometric Survival Model

Abstract

The banking sector is constantly evolving, seeking effective ways to attract and retain clients, especially those with high financial potential. One of the ways to achieve this goal is to provide car loans at low interest rates, such as 0.01%. However, the untimely outflow of clients after repayment of the car loan becomes a significant problem for banks leading to the loss of potential income from other banking services. The research aims to evaluate the impact of selling additional banking services on increasing clients' activity duration. The research used statistics on opening new bank clients, whose first product was a car loan at an interest rate of 0.01%, from 2018 to 2022. The dataset included 9,224 records. The Cox proportional hazards model is used to determine the impact of a credit card on the duration of car loan client activity. The analysis of the model coefficients showed that with a credit card, clients closed at a rate of 0.86 of the rate of closing clients without a credit card. However, during the verification of the proportional hazard assumption, it was determined that the credit card's influence level changes significantly over time, indicating the model's inadequacy. The next phase of the study was the search for an influencing parameter that meets all the quality conditions of the Cox model. Having a credit card with at least one transaction was selected. For this model variation, all indicators of model adequacy were met. The coefficient estimation results showed that clients with an active credit card closed at a rate of 0.36 of the rate of closing clients without it. The evaluation of the active credit card impact confirms that selling a credit card allows for an increase in the bank clients' activity duration. However, a critical success factor is the sale of a credit card and its activation. The obtained research results can be used to optimize the bank's marketing and sales strategies, ensure more effective customer retention and increase the bank's profits.