Calculating and communicating tail association and the risk of extreme loss

In this paper we examine two aspects of extreme events: their calculation and their communication. In relation to calculation, there are two types of extreme events that are considered.

The first is the extent to which extreme events in two or more variables occur together. This can be gauged by using measures of tail association. Higher levels of tail association are useful for highlighting the extent to which there are concentrations of risk. We investigate the range of approaches used to measure tail association and propose a pragmatic alternative, the coefficient of finite tail dependence.

The second type of extreme event arises from combinations of losses from a series of risks that together result in total losses exceeding a particular level. This is measured using ruin lines or, in higher dimensions, planes and hyperplanes. The probability of ruin and the economic cost of ruin are considered here. In this context, it is important to consider what the term “loss” actually means, and whether it is in relation to a current set of exposures or a potential strategy.

The communication of extreme events is discussed not just in terms of the numbers that can be used, but in terms of the graphical methods that can be used to aggregate information on a range of risk combinations. This involves communicating not just the level of risk but also the importance of the risk considered.