Long-Term Returns in Stochastic Interest Rate Models: Applications

We extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalized Bessel-square processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral fg rudu. For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.