Operational Risk Loss Distribution

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Hi David,

1. Extreme losses in the tail of the operational risk distribution will follow EVT or GPD. i am unable to link the both.

2. Heavy tails need large sample size to give the correct output . How do we link it to condfidence intervals.

am getting confused in the above mentioned concepts.

Rgds
Souvik

 

[David Harper CFA FRM]

Hi Souvik,

The context is a little loose but:

1. A primary theme in operational losses is the lack of data in the low-frequency, high severity (e.g., catastrophes) tail: whereas in the case of market risk VaR, a company can typically find at least some large losses in its history, it may have few or no big operational losses. (hence the need to complement with external/consortium data). EVT tries to "rescue us" by giving us a parametric function to use in the tail, instead of trying to use actual (empirical) data. Technically, we use Dowd so the concepts are:
* EVT is the theory with two approaches (older block maxima and newer peaks over threshold, POT)
* Where block maxima approach (max losses in time slices) implies a GEV distribution and
* POT approach (losses over a threshold) implies a GPD distribution.
* So, put another way, EVT gives us a GEV or GPD distribution to use in the tail.

2. We still tend to need data to parameterize the GEV/GPD function; just like we need historical return data to produce a variance/volatility. The more data, ceteris peribus, the better the parameters.
But this all concerns the FIRST STEP: to arrive at the specification of the distribution.
Once we have specified at distribution, then we can create confidence intervals.

Hope that helps, David