Monte Carlo simulation of present value of cash flows

Abstract

This paper is concerned with financial application of Monte Carlo simulation of infinite series. In fact, present value of a cash flow is represented as infinite series. Hence, the Monte Carlo may be applied to approximate the present value. It is seen that the Monte Carlo method is sample approximation of the mean of cash flow computed at a stopping time. The stopping time, first, is considered as an up-crossing time point of sequence of uniform random variables and then it is replaced by up-crossing of macro-economic variables (called as factor) which brings the dependency structure to the problem which is modeled by auto-regressive to any things (ARTA) models. Here, two different Monte Carlo simulation methods are presented. A financial application is also given. Continuous time extensions of results are also proposed. Finally, a concluding remark section is given.