Estimating Uncertainty in Cash Flow Projections

In order to be complete dynamic financial analysis (DFA) models should deal with both the amount and timing of future loss and loss adjustment expense payments. Even more than asset cash flows, these future payments are very uncertain. This paper begins by estimating both process and parameter uncertainty in reserves for annuity-type benefits such as available in some automobile no-fault states or in workers compensation. Arguably, such reserves have underlying distributions (inherent in the mortality models) that may be more easily understood and treated than many other casualty coverages. We explore the estimation of both process and parameter uncertainty for this example. In the process we derive formulae that can be used to model uncertainty in other applications, once the various parameters are estimated. Many of the estimation methods covered should generalize to non-annuity applications. There is also a companion of this paper, titled “Modeling Parameter Uncertainty in Cash Flow Projections” that provides motivation for the estimates contained in this paper. In that paper we discuss approaches to modeling future cash flows and argue for separation of parameter and process uncertainty as well as describing methods to model them both.