Stochastic Upper Bounds for Present Value Functions

Abstract

In most practical cases, it is impossible to find an explicit expression for the distribution function of the present value of a sequence of cash flows that are discounted using a stochastic return process.In this paper, we present an easy computable approximation for this distribution function. The approximation is a distribution function which is, in the sense of convex order, an upper bound for the original distribution function. Explicit examples are given for pricing stochastic annuities with stochastic return process, more general stochastic cash flows as well as pricing Asian options. Numerical results seem to indicate that the approximation will often be rather close to the original distribution function.