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Wesley_Willis
11-30-2009, 07:48 AM
Is there a generally used approach to calculating the individual VaR percentiles needed on different risk pools (e.g., several lines of insurance or even different policy years for one line) in order to estimate an overall VaR? I don't think that using a straight percentage of, say, 95% for each component would correspond with an overall percentile of 95%.

RocBoys
11-30-2009, 07:56 AM
Get a distribution (non-parametic easier to work with) of the overall portfolio and get your percentiles and other fancy numbers directly from there.

tommie frazier
11-30-2009, 08:27 AM
it is doubtful they combine in a nice way. load em into a simulation package and then get the combined VaR. after estimating correlation between them

silverfox
11-30-2009, 09:36 AM
I agree you probably have to simulate it.

whisper
11-30-2009, 11:46 AM
Is there a generally used approach to calculating the individual VaR percentiles needed on different risk pools (e.g., several lines of insurance or even different policy years for one line) in order to estimate an overall VaR? I don't think that using a straight percentage of, say, 95% for each component would correspond with an overall percentile of 95%.

You're correct that the sum of the 95% individual values do not equal the 95% portfolio. Unless you're dealing with a select number of curves, aggregating distributions rarely lead to tractable formulas. The best solution is to simulate.

campbell
12-01-2009, 08:17 AM
You can use copulas if you've got a correlation structure in mind for these different sub-groups, but you're going to have to directly check via simulation how that correlation structure shakes out.

For a default, I'd use a Student-t copula, and you can probably figure out correlations and degrees of freedom to get it to fit well enough to your models.