# Distribution of risk factors with mean-reversion properties

I'm trying to figure out a way to determine if a given change in a risk factor, such as a volatility node on a surface, or a basis spread on a curve or an FX rate etc. as well as equity prices can be considered abnormally large.

We generally accept at face value the supposition that stock returns are normally distributed so it seems simple enough here to estimate the volatility of the stock returns for the equity and then compare the given change to see if change is an extreme event or not for the time series. What would be a good way to do the same for the other risk factors, I'm assuming that volatility for example would be mean reverting but would it still be reasonable to treat it the same way? I want a way to get an approximate answer for all the risk factors treating them (at least almost) the same, so fitting a stochastic process to each of them seems out of the question unless it can be done in a very generalized way. Is there a better (but still simple) way to do this than just treating the changes as normal and ignoring the mean-reverting properties?

• A simplistic way would be to compare it to the distribution of the historical changes. Say a rate moved by 2bps, then one can look at its history - e.g., when was the last time a move of this magnitude happened, how often does a move of >2bps happen. Hope this helps! – Magic is in the chain Apr 17 at 19:27