On Short-Term Loan Interest Rate Models: A First Passage Time Approach

In this paper, we consider a stochastic diffusion process able to model the interest rate evolving with respect to time and propose a first passage time (FPT) approach through a boundary, defined as the “alert threshold”, in order to evaluate the risk of a proposed loan. Above this alert threshold, the rate is considered at the risk of usury, so new monetary policies have been adopted. Moreover, the mean FPT can be used as an indicator of the “goodness” of a loan; i.e., when an applicant is to choose between two loan offers, s/he will choose the one with a higher mean exit time from the alert boundary. An application to real data is considered by analyzing the Italian average effect global rate by means of two widely used models in finance, the Ornstein-Uhlenbeck (Vasicek) and Feller (Cox-Ingersoll-Ross) models.