I have a large simulated loss data (from catastrophic models developed at my school) to calculate some extreme quantiles. Previously they used non-parametric methods to do this (find the point estimate for these extreme quantiles and CIs).
I am using parametric models (extreme value theory, fat tail distributions, etc.) to do it. I have been thinking about the pros and cons for these two methods.
I would appreciate if someone could provide some summaries of parametric and non-parametric models, their advantages and disadvantages.