We're using extreme value theory to model tail risks on our portfolio. After we choose the threshold, we fit generalized Pareto distribution to our data over the threshold. The expected value of GPD is quite larger (10%) than the average value of our losses over the threshold. My question is, is this to be expected? Or does that mean that the GPD is a bad fit to the data and that we've chosen the wrong threshold? Also, is there a good way to check whether the GPD is a good fit?
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