An application of comonotonicity and convex ordering to present values with truncated stochastic interest rates

A subject often recurring in recent financial and actuarial research is the investigation of present value functions with stochastic interest rates. Only in the case of uncomplicated payment streams and rather basic interest rate models is an exact analytical result for the distribution function available. In the present contribution, we introduce the concept of truncated stochastic interest rates, useful to adapt general stochastic models to specific financial requirements, and we show how to obtain analytical results for bounds for the present value. We elaborate our method in extension for the Hull and White model and related models. We illustrate the accuracy of the approximations graphically, and we use the bounds to estimate the Value-at-Risk.