P1.T4 Ch 6. X percentile for capital calculation

[FPare4571]

Hi David,

Just trying to wrap my head around the connection between the LogN and the N distributions when it comes to the X percentile for capital calculation. My confusion stems from the fact that the X percentile is explained based on the LogN distribution for loss over one year (depicted in Figure 6.2) whereas the calculation is based on the N distribution: am I right thinking that even though the X percentile e.g. 99.9 % Basel is calculated based on the N distribution and it does not correspond to the 99.9% percentile in the LogN?

 

[gsarm1987]

@FPare4571 please allow me to answer: The X percentile used for capital calculation can be based on the Normal distribution or the LogNormal distribution. It depends on the context and the underlying assumption about the distribution of data. Percentiles in both distributions represent the value below which a certain percentage of the data falls.

Normal distribution is indeed a simplification for risk modeling in many cases, but when we are dealing with data that follows a Log-Normal distribution, percentiles are calculated based on that distribution, not the Normal distribution.

like in Basil II, default risk calculated at 99.9% confidence level for one-year time horizon similar to IRB approach

Basel III, the calculations are typically performed based on the Normal distribution (N) assumption, not the LogNormal distribution (LogN). The reason for this choice is often for simplification and regulatory consistency.