Copulas and Value-at-Risk

Abstract

The conventional procedure of approximating risk factors with multivariate normal distributions implies that the risk’s dependence structure is reduced to a fixed, predetermined type. Even if the autocorrelation structure of the risk factors is neglected, stipulating a multivariate normal distribution means that the following assumptions hold:

• 1. symmetric distribution of returns

• 2. the tails of the distribution are not too heavy

• 3. linear dependence

The first point is discussed in Chapter 3. The second point is not empirically proven, since in general the tails of the distribution display leptokurtic. The third point deals with the properties of the covariance (correlation): high correlation means that there is almost a linear relationship among the risk factors. Although there are many reasons against this procrustes type assumption of a normal distribution, there are a number of practical reasons, which in particular are associated with performing the calculations, Embrechts, McNeil and Straumann (1999a) and Embrechts, McNeil and Straumann (1999b).