Jul 24

Parametric versus empirical distribution – 8 min screencast

by David Harper, CFA, FRM, CIPM

In risk measurement, we often deal with the question of whether to employ a parametric or empirical distribution. The FRM candidate will note Deutsche Bank's ("LDA at work") approach to modeling operating losses combines both in a so-called piece-wise construct:

Empirical distribution for the body of the severity of operational losses; losses < $50 million
Parametric distribution for the tail of the severity of operational losses; losses > $50 million

In this brief screencast, I use a much simpler example merely to highlight the difference:

My parametric approach is a normal distribution with mean of 0 and standard deviation of 5. Based on only these two parameters, I can generate 100 randomized losses (that's the advantage of parametric approach: I only need to pick the distribution and specify the parameters)
My empirical approach also generates 100 random losses, but instead generates the losses via a so-called statistical bootstrap: armed with a set of 100 historical gains/losses, I simply select 100 randomly with replacement

Importantly, the empirical approach does not need parameters but, on the other hand, requires a dataset (that's why Deutsche Bank can't really use empirical in the extreme tail, there just isn't enough data from which to generalize). Further, while my normal will fail to give fat tails (leptokurtosis), my empirical is not confined to skinny tails.