28 Extreme Value Theory
Peter McQuire
28.1 Introduction
Risk actuaries and analysts allocate much of their time to assessing the likelihood of particular events occurring which could result in severe financial consequences to an institution, and then implementing procedures to manage these potentially catastrophic risks. Extreme Value Theory (“EVT”) is a branch of mathematics which can help with analysing these risks.
Risks can broadly be assessed in two ways – qualitatively and quantitatively. This is particularly true of extreme risks. In situations where there is little available data, a quantitative analysis is unlikely to yield results which are statistically credible, thus requiring a qualitative approach to be adopted. Development of quantitative models to analyse such extreme, infrequent events is clearly problematic. For example we may want to assess the risk of bank insolvency resulting from internal fraud; as there is relatively little data on such events a qualitative approach is likely to be required.
However, when we have sufficient historic data at our disposal, a quantitative approach may be possible; the total volume of data may be such that, even for extreme events, we have an adequate amount of data. For example:
- an equity manager may wish to estimate maximum daily losses that could reasonably be expected from the equity portfolios she is managing; the example included later in the chapter ...