ROBUST EXTERNAL RISK MEASURES

Choosing a proper risk measure is an important regulatory issue, as exemplified in governmental regulations such as Basel II accord [1] and its recent revision [2], which use Value-at-Risk (VaR) with scenario analysis as the risk measure for setting cap-ital requirement for market risk. The main motivation of this article is to investigate whether VaR with scenario analysis are good risk measures for external regulation. By using the notion of comonotonic random vari-ables studied in decision theory literatures such as Refs 3–8, we shall propose a new class of risk measures satisfying a new set of axioms. The new class of risk measures includes VaR with scenario analysis, in particular the current and recently revised Basel II risk measures [1,2] as special cases, and therefore provides a theoretical basis for using VaR with scenario analysis as robust risk measures for the purpose of external, regulatory risk measurement. Broadly speaking, a risk measure attem-pts to assign a single numerical value to a random financial loss. Obviously, it can be problematic to use one number to summarize the whole statistical distribution of the financial loss. Therefore, one shall avoid doing this if it is at all possible. However, in many cases there is no other choice