[nabla9]

For synthetic distributions Mandelbrot's Multifractal is good enough.

You may consider using real historical distributions derived from real data. You can record different distributions from different time periods and different economic conditions.

[billziss]

Thanks for your answer.

I am using real data of course, but I am also seeking a deeper understanding and ideally one based on first principles. This is why I asked this question.

It seems to me that if we could correctly characterize the dependence of the returns we could perhaps arrive at the correct theoretical answer that also coincides with practical observation. Mandelbrot almost gets there, but his use of multifractal trading time seems brilliant but also somewhat arbitrary (at least in the papers of his I read).