Accumulated (integrated) interest and the square root process

Purpose: The purpose of this study is to determine distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process. Design/methodology/approach: The law of iterated (or double) expectations is used to determine the mean and variance of the accumulated rate of interest on a cash management (or loan) account when interest accumulates at the instantaneous rates of interest implied by the square root process. Findings: This study demonstrates how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function. Originality/value: This study has strong educational value in determining distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process and demonstrating how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.