6.1 Motivation

When we design a value-at-risk (VaR) measure, one of the first steps is to choose a key vector ¹R. We need this before we can design a mapping procedure that will construct portfolio mappings ¹P = θ(¹R). We also need it before we can design an inference procedure that will characterize the conditional distribution of ¹R.

There are various issues to consider in selecting what prices, interest rates, spreads or other variables to represent with key factors ¹R_i. One of these is the availability of historical market data. An inference procedure requires historical data related to all key factors. If there is no historical data relating to a particular variable, it makes little sense to model that variable as a key factor.

In this chapter, we discuss types of historical market data that may be used by value-at-risk measures. We describe how data is collected over time, how it is filtered and cleaned of errors, and how it is converted into forms usable by an inference procedure.

Exhibit 6.1: A reproduction of Exhibit 1.12, which is a general schematic for value-at-risk measures. The availability of historical market data influences the selection of financial variables to be modeled with key vector ¹R. This, in turn, influences our design of both a mapping procedure and an inference procedure.