Q.30 Salim Abdalla, FRM, is the CRO at an Iranian bank. For some time now, the bank has used internal models generally governed by the central limit theorem, but Abdalla is worried the existing models may not be addressing the possibility of random extreme losses that could create a major destabilizing effect. In a bid to stir change, he recommends the use of extreme value theory. While discussing EVT with one of his colleagues, the following statements are made:

I. To apply the EVT, the underlying loss distribution can be any of the commonly used distributions, e.g. normal or lognormal, and will usually be unknown
II. If the tail parameter of the generalized extreme value (GEV) distribution goes to zero, then the GEV essentially becomes a Gumbel distribution
III. If the tail parameter of the generalized extreme value (GEV) distribution is less than zero, the GEV becomes the normal distribution
IV. As the threshold value is increased, the distribution of exceedances converges to a generalized Gumbel distribution

Which of the statements above are incorrect?