2.1. CHAPTER OVERVIEW

The ultimate goal of this and the following two chapters is to establish a framework for modeling the non-normal conditional distribution of the relatively large number of assets that make up the financial portfolio of a company. This is an ambitious undertaking, and we will proceed cautiously in three steps following what we will call the stepwise distribution modeling approach (SDM). The first step of the SDM is to establish a variance forecasting model for each of the assets individually and to introduce methods for evaluating the performance of these forecasts. The second step is to link the individual variance forecasts with a correlation model. The variance and correlation models together will yield a time-varying covariance model, which can be used to calculate the variance of an aggregate portfolio of assets. Finally, the third step will consider ways to model conditionally non-normal aspects of the assets in our portfolio that is, aspects that are not captured in the conditional mean and variance.

The second and third steps are analyzed in subsequent chapters, while the first step is covered in this chapter in the following manner:

1. We briefly describe the simplest variance models available including the so-called RiskMetrics or exponential smoothing variance model.

2. We introduce the GARCH variance model and compare it with the RiskMetrics model.

3. We suggest extensions to the basic model, which improve the ability to capture variance persistence and leverage effects. We also consider ways to expand the model to take into...