
How to estimate risk in extreme market situations
Estimating portfolio risk in extreme situations means answering two questions: First, has the market entered an extreme state? Second, how are returns likely to be distributed in such an extreme state? There are three different types of models to address these questions statistically. Conventional “extreme value theory” really only answers the second question, by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. “Extreme value mixture models” simultaneously estimate the threshold for extreme distributions and the extreme distribution itself. This method seems appropriate if uncertainty over threshold values is high. Finally, “changepoint extreme value mixture models” even go a step further and estimate the timing and nature of changes in extreme distributions. The assumption of changing extreme distributions across episodes seems realistic but should make it harder to apply the method out-of-sample.








