Market Risk VaR: Historical SImulation Approach

Question

What is extreme value theory? (EVT)

Answer 1

It's a branch of statistics that deals with:

1. extreme events: magnitude is far from what we usually observe

2. rare events: occurrence over time is scarce.

Answer 2

ES tells how much can be expected to be lost when things go bad

Answer 3

1. Block Maxima (B.M.)

The observations are divided into blocks and, for each block, only the maximum (or the minimum) value is considered. the distribution of the rescaled maxima is shown to be the GEV, sheet 6, slides 9.

2. Peaks over threshold (P.O.T.)

A threshold u is defined, and only the observations overcoming that threshold are taken into consideration. In this case the distribution of the rescaled maxima is the GPD, sheet 7, slides 9.

Answer 4

There are different methods, but heuristically, we can say that:

- u should be greater than the 95% percentile of the empirical distribution.

- u should be the value for which the emplot and the meplot show some sort of linearity.

Answer 5

When we study the loss distribution we have a particular interest for large risky losses, which can be seen as exceedances over a threshold and we may use the GPD to approximate the tails.

The theoretical approximation with the GPD makes sense because, in general, we have just a few empirical observations of extremely large losses.