I got asked this question during an interview with a bank for their market risk department:
You have a large set of historical data on stock price, however there are very limited data in the tail(say beyond the 95% percentile). Assuming you don't have the distribution for the data, how do you estimate/predict the tail/extreme events.
I was thinking about maximum likelihood estimation since I was given the data and I just need to calibrate the parameters so that $$L(\theta|x_1, X_2...X_n)$$ is at maximum.
But does it mean I need use non parametric methods?
I assume this is more of a open ended question, so any thoughts will be welcomed :)