Stock prices surely have finite variance... but itβs true that it can be high enough to be problematic and if you choose to use an infinite-variance distribution to model prices you may need to pay attention to the consequences.
Re:The Central Limit Theorem and Sampling
by deepsun on Wednesday July 10, 2019 @01:58AM
(#20399478)
> Stock prices surely have finite variance.
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.
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?
Nope. Not true for all the distributions. For example, stock prices cannot be used in central limit theorem.
Distributions must have second moment, in other words, have finite variance.