Value-at-Risk: Theory and Practice

When we design a 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 = ?( 1 R). We also need it before we can design an inference procedure that will characterize the conditional distribution of 1 R.
There are various issues to consider in selecting what financial 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 financial 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 VaR 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.
Data can represent market prices, interest rates, spreads, implied volatilities, etc. Any of these may be directly quoted in the markets, or they may be inferred from other quantities that are directly quoted. All are, in some sense, prices. Price data can vary with respect to type, method of collection, and source.