The Basel Multiplier

Chebyshev's Inequality says:

Suppose we wanted the highest VaR at the 99 percent confidence level.

That means, only 1 percent of samples taken should have VaR that exceed this level. Without making any assumptions about the distribution, Chebyshev's inequality says that we can expect K = 10 at the 1% tail end.

Granted, that's pretty big, but if we assume the distribution is symmetric then we can divide the righthand of the equation by half and the new k becomes about 7.

So if a financial institution had assumed a normal distribution, the k value for which VaR is not exceeded with 99% confidence is closer to 2.36. Dividing our earlier k (=7) by this k value, we get ~3. Thus the correction multiplier is about 3.

Example taken from Jorion