Do you really think there is a non-zero probability of the price of a stock, say Apple, closing today over $1000? Over $1mn? Over $1bn? Over $184467440737095516.15 which is the largest number of cents that can be stored as a 64-bit integer? Over 10^100 dollars?
Are you sure? On my data, they are most closely modeled by Pareto distribution (infinite variance).
As far as I remember, that was discovered by Mandelbrot, studying cotton stocks.