Stochastic Interest Rates Model in Compounding

Abstract

Interest rates considerations in cash flows are fundamental concepts in finance, real estate, insurance, accounting and other areas of business administration. The assumption that future rates are fixed and known with certainty at the beginning of an investment, is a restrictive and theoretical assumption that is not obtainable in real situations. A more realistic approach would be, to report the expected future value and its variance for a given return process. This paper derives formulae for the mean and variance of future values for a single cash flow and sequences of cash flows when returns processes are randomly and independently distributed. Numerical examples are given to illustrate the magnitude of the change from the fixed rate of return process to stochastic (random) rate of return processes.