Alpha Stable Distributions

I am doing some work with return distributions. In a previous gig we did a lot of work on this subject, and I was really encouraged by the track of work we were following.

A quick recap: we know that trading returns do not typically follow a normal Gaussian distribution path, yet most of the models in modern day finance still use these less than perfect solutions. Its typical human nature, the solutions give us a nice elegant quick solution most of the time. Because a more accurate solution is more difficult to figure out we rather dismiss the facts that bad things happen more often than we anticipate in the name of progress.

We were determined to find a more realistic solution, in keeping with my previous post, keeping it real 🙂 .

In the 2 charts I am going to illustrate how our most likely estimate (MLE) model using Alpha Stable Levy distributions does a much better job than the blue line normal distribution model.

fitted distribution

fitted distribution 2