Value at Risk by Philippe Jorion

Author:Philippe Jorion
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2007-04-05T04:00:00+00:00

FIGURE 12-4

Comparison of distributions.

To illustrate, Figure 12-4 compares a distribution for two variables only (after all, this is the number of dimensions of a page). The figure shows, on the left, pseudorandom points and, on the right, a deterministic, low-discrepancy sequence obtained from a so-called Sobol procedure.10

The left graph shows that the points often “clump” in some regions and leave out large areas. These clumps are a waste because they do not contribute more information. The right panel, in contrast, has more uniform coverage. Instead of drawing independent samples, the deterministic scheme systematically fills the space left by the previous numbers in the series.

Quasirandom methods have the desirable property that the standard error shrinks at a faster rate, proportional to close to 1/K rather than for standard simulations. Indeed, a number of authors have shown that deterministic methods provide a noticeable improvement in speed.11 Papageorgiou and Paskov (1999) compare the computation of VAR for a portfolio exposed to 34 risk factors using 1000 points. They find that the deterministic sequence can be 10 times more accurate than the Monte Carlo method.

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