Ask HN: Probability Distribution of Stock Returns
It is relatively easy to deduce that under idealized conditions stock returns follow a log normal distribution. One arrives at this by considering the product of ratios of prices ("stock returns"), applying a natural logarithm to convert the product into a sum and then applying the Central Limit Theorem under the condition that the ratios are iid (independent and identically distributed) and have finite mean and variance.
The problem is of course that we cannot just assume that returns are iid or that they have finite variance. So I am seeking alternative theories that try to address these shortcomings.
I am aware of Mandelbrot's Multifractal Model of Asset Returns. Is this considered SOA in the field? Is there something else that is considered a better model or easier to work with?