I was wondering what the most common, or most popular, ways - in both academia, and industry - there were to model the fat tails of volatility in asset prices changes.

I am presuming a basic Brownian motion random walk, is not what is used, because it will not replicate fat tails. Is that correct? Or am I wrong, and in most cases, a basic Brownian motion is "good enough"? What are more advanced methods that are used, whether it be in terms of stochastic calculus, statistical methods, etc.?

  • $\begingroup$ Are you interested in discrete time or continuous time? Or both? $\endgroup$ Dec 13, 2021 at 8:46
  • $\begingroup$ I would be interested in either, whatever methods are in common use. I do not know enough about the industry to know what is currently in popular use, or in which circumstances you might prefer one over the other. $\endgroup$
    – Tristan
    Dec 13, 2021 at 9:51
  • 1
    $\begingroup$ Accepted. Sorry, I assume I was just waiting for more answers and then forgot about the thread. $\endgroup$
    – Tristan
    Apr 18 at 17:25

1 Answer 1


For the case of discrete time, consider a GARCH model with standardized innovations that follow a Student-$t$ or another (somewhat) heavy-tailed distribution. The dependent variable will have a tail heavier than that due to the GARCH model. (The model generates heavier tails than present in the distribution assumed for the standardized innovations.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.