A basic assumption in BS and most models can be loosely stated as
“Daily stock returns are normally distributed, approximately.” I used
to question this assumption. I used to feel that if the 90% confidence
interval of an absolute price change in IBM is $10 then it will be
that way 20 years from now. Now I think differently.
When IBM price was $1, daily return was typically a few percent, i.e.
a few cents of rise or fall.
When IBM price was $100, daily return was still a few percent, i.e. a
few dollars of rise or fall.
So the return tends to stay within a narrow range like (-2%, 2%),
regardless of the magnitude of price.
More precisely, the BS assumption is about log return i.e. log(price
relative). This makes sense. If %return is normal, then what is a