A stochastic model for loan interest rates

Abstract. The topic of interest rate restrictions and their legal implications represents a delicate subject about which a recent inventory of EU authorities was developed. This is aimed to inspection of the so called principle of "good morals" against usury for the Member States. The most recent Italian law regulating legal rates of interest applied in loans, sets a threshold under which loan interest rates have to remain for being nonusurious, in the sense that if the loan rate lies outside the threshold, it becomes a usury rate and has to be prosecuted. The threshold is stated by Bank of Italy precisely each three-month period. In the paper the authors propose a stochastic process modelling the non-usurious interest rates applied in loans, in order to control its quarterly behavior. It is studied in the form of a modification of the Cox, Ingersoll and Ross model moving between two bands and closed expressions for its expected value and variance are given both conditional and unconditional. The model parameters are estimated by the Indirect Inference Method; the behavior of the expected value and variance functions are illustrated.