ABSTRACT
The definition of economic capital as introduced in Chapter 1 appears fully satisfactory at first glance. Starting with the path-breaking paper by Artzner et al. [11], several studies revealed a number of methodological weaknesses in the VaR concept by drawing up a catalog of mathematical and material attributes that a risk measure should fulfill, and proving that the VaR concept only partly fulfills them. Risk measures that satisfy these axioms are called coherent. Before we describe their basic features in the next section, we briefly reiterate the main notations (cf. Chapters 1 and 2):
The portfolio loss variable (compare Equation (2.51)) is given by
L =
wiηiLi,
where
are the exposure weights, so all portfolio quantities are calculated in percent of the portfolio’s total exposure. The severity is abbreviated to ηi = LGDi; Li = 1Di are Bernoulli random variables with default events Di. Accordingly, the default probability (e.g., for a one-year horizon) for obligor i is given by
PDi = P(Di) .
