Usage of Statistics in Quantitative Risk Models

Christian Meyer and Peter Quell

In the previous chapter, the basic elements of QRMs were introduced. As a reminder, these are:

• a quantity of interest, the future value of which is uncertain;

• a set of potential future scenarios that describe possible values of that quantity of interest; and

• a statistic or risk measure to sum up the essential information obtained from the analysis of the potential future scenarios.

This chapter will explore how such an abstract framework can be implemented in practice, focusing on the set-up of a QRM that could be used in the financial markets, although the basic principles are transferable to other applications as well. The usage of statistics in QRMs is unavoidable in practice, and possible issues will be illustrated through examples. Finally, categorisations of risk and uncertainty will be presented, and there will be a discussion on if – and to what extent – statistics can help in QRMs.

SET-UP OF QUANTITATIVE RISK MODELS

The typical set-up of a QRM used by participants in financial markets is summarised in Figure 2.1. Starting from a current portfolio of financial instruments, such as equities, options and bonds, one needs to ask which profits or losses