Stochastic jumps do occur – the problem with such things is that they are not predictable. Perhaps what the NYU team is missing is the right language – the characteristics of the underlying process of the movement of the zebrafish appear to have stochastic jumps in it. But that has nothing to do with stock market modeling – an oxymoron. The reason the zebrafish is jumping stochastically is the same why stock markets do at times – arrival of new information. And, by definition these are not predictable.
As trillion $ slosh around an industry with no value added to society, further research toward predictions of stochastic jumps seems unwarranted.