The very notion of accuracy and the acceptability of a measurement, observation, description, count, is inseparably tied to the use to which it is to be put.
Oscar Morgenstern, On the Accuracy of Economic Observations
In this chapter we discuss the generation of forward-looking scenarios describing uncertainty in the states of an economy and in the financial markets. Disparate sources of risk are integrated in a common framework, and time information is also incorporated. These scenario generation methods provide the data needed to implement the optimization models discussed in previous chapters. Scenarios and their properties are discussed first, followed by a general framework for building scenario generation models for both assets and liabilities. Three scenario generation methods are then introduced, using either historical data or mathematical models. These methods are suitable for the generation of scenarios for single-period optimization models. The chapter concludes with methods for constructing event trees for multi-period, dynamic, portfolio optimization models.
9.2 Scenarios and their Properties
The models in this book address optimal decision making in the face of uncertainty. Uncertainty is treated using discrete random variables together with the associated probabilities. As time evolves in discrete steps, the random variables take one of a finite set of values. This set is the sample space, and its elements are indexed ...