### Chapter 6

#### Historical Market Data

# 6.1 Motivation

When we design a value-at-risk (VaR) measure, one of the first steps is to choose a key vector ^{1}** R**. We need this before we can design a mapping procedure that will construct portfolio mappings

^{1}

*P*= θ(

^{1}

**). We also need it before we can design an inference procedure that will characterize the conditional distribution of**

*R*^{1}

**.**

*R*There are various issues to consider in selecting what prices, interest rates, spreads or other variables to represent with key factors ^{1}*R _{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.

^{1}

**. This, in turn, influences our design of both a mapping procedure and an inference procedure.**

*R*