# How to simulate asset returns using student t?

I am currently trying to simulate an asset return using the student-t distribution, but I can't find how I should do this. I began with the Geometric Brownian motion and just changed in order that epsilon follows the student-t distribution instead of the normal distribution, but I found out that this is not the correct way, I read a lot about levy-processes, but I don't know exactly how do simulate such returns.

Thank you very much in advance

• In Continuous Time it may not be possible AFAIK (since sum of two Student-t increments is not necessarily Student-t), but in Discrete Time it is easy and frequently done. – noob2 Jul 19 '16 at 13:20

You will need a 'pseudo' random number generator - most stats programming languages have them (Matlab, R, Python...). But GBM is defined with Normal increments $N(0,\sigma^{2}(T-t))$ so I dont think using Student's t distribution is a good idea, never seen it in any literature/applications. It is however used for instance in GARCH modelling....